Autodetect radians/degrees. I tried to use euler rule but the answer is strange. How to incorporate scientific development into fantasy/sci-fi? You seem to say that $\arg i=\pi/2+2\pi ik$. @Argon I know that, but it is still true, the argument of $i$ is $\frac{\pi}{2}$. How to plot a curve in complex plane that include e constant. @ncmathsadist: I see; you're saying it is essentially because $\sin$ is periodic? The loop can best be categorized as a: a. As noted in particular by L.F., Argon and ncmathsadist, the answer depends on the branch of the complex logarithm you choose to work with. I think I was on the wrong path to the right number, if I had considered the order doesn't matter you get 2x-2x^2 as the probability, integrate from [0,1] to … e^5, is bigger than e^1. Alexis needs to buy 300 sheets of paper. An updated version is available every six months. @EricStucky Actually $i^i$ is not a real number, it is either undefined or a subset of the real line. Redemption tables allow you to find the values and interest earned for Series EE savings bonds, Series E savings bonds, Series I savings bonds, and Savings Notes issued from 1941 to present. What is imaginary infinity, $i\lim\limits_{x \to \infty} x = i\infty$? It is not well-defined. I mean, we can take $5\pi/2$ and get a different answer? For example, a $100 I bond would be 4 times the value listed in the chart. i = i + 1 1. Therefore for $z=i$ we get that $\ln i = \frac{i\pi}{2}$ since $\arg i = \frac{\pi}{2}$. It can be because of Euler’s Formula . Transcript To determine the value of i raised to a power greater than two, we rewrite the term using exponent rules.Remember that i^2 = -1 and i^4 = 1. However, |e^1000000i| is still just 1. I think it should be mentioned that $e^{-\frac{\pi}{2}}$ is the. The 3rd i is affected by the increment. Does any Āstika text mention Gunas association with the Adharmic cults? Penny . Current Values. The value of $i^i$ - is my method contradictory? How to learn Latin without resources in mother language. An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i 2 = −1. It might be strange at first , but yes it is a real number under the principal branch. I I A. Are you familiar with $e^{ix}=\cos x+i\sin x$? Yes, as L.F. said, log i can produce an infinite number of values, and is only a function upon selecting a branch $i(\frac{\pi}{2} + 2\pi n). $$i^{i} = e^{-\pi/2 + 2k \pi}, \;\; k \in \mathbb{Z}$$, site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. How can a number be multiplied an imaginary amount of times? The value of i is the square root of -1, or √(-1). Wolfram Alpha says that it is equal to $e^{{-\pi}/{2}}$, but how would you arrive at that answer? Simple... you compiler is evaluating BOTH increments before performing the sum, without caching the intermediate results. How do they determine dynamic pressure has hit a max? Value of i The value of i is √-1. (that is the principal angle) This matches your result. log (i) has a value of approximately 0.68i, which would give: x = i^i log (x) = i log (i) = i i*0.68 = -0.68 x = 10^ (-0.68) = approximately 0.2079. (However, while the square roots of a number always have the same magnitude even if they differ in sign, the values of have different magnitudes). (However, while the square roots of a number always have the same magnitude even if they differ in sign, the values of have different magnitudes). rev 2021.1.8.38287, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Missing a minus sign, but that's the right idea. The principal value of would be --the case where n=0. So this exponent is pi*(-1)/2 ) e^(-pi/2)=0.2079. The square of an imaginary number bi is −b 2.For example, 5i is an imaginary number, and its square is −25.By definition, zero is considered to be both real and imaginary. The value of 'i' is just 'i'. Method 1 (Naive : O(n 2)) The proofs of limit laws and derivative rules appear to tacitly assume that the limit exists in the first place. What is the earliest queen move in any strong, modern opening? This means that when you add i twice, it now has the value of 7. Thank you. 1 decade ago The value of i is the square root of -1, or √ (-1). Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Can 1 kilogram of radioactive material with half life of 5 years just decay in the next minute? [How to figure out without brute force], Looking for a short story about a network problem being caused by an AI in the firmware. (Photo Included). ( ̂ × ̂) + ̂. What's the link between logarithms and the zeroth power, if any? so we get.. j=10+(11) =21 taking the log of $a^b$ (Project Euler problem 29). Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their … Imaginary Numbers are not "Imaginary". So we have: What Constellation Is This? -8 B. Click hereto get an answer to your question ️ What is the value of i^i Where i = √(- 1) It only takes a minute to sign up. i^i=e^(-pi/2) (multipling the exponent by i raises to the power of i .and i*i=-1. $ $e^{-\pi/2}$ is the principal value with $n=0$. Power by imaginary numbers do not change the size of the result. The map $z \mapsto z^i$ needs to be defined as $z \mapsto e^{i\log(z)}$. How many things can a person hold and use at one time? Increment i (i becomes 1) Assign the value of step 1 to i (i becomes 0) Not that the increment is being discarded. Thus to look at i i one could consider i i = (e i π /2) i and that's the same as e (i π /2)i = e (i 2)(π /2) = e-π /2. There are actually an infinitude of values. Penny . What is the smallest value of n such that an algorithm running at 100*n^2 operates faster than 2^n ? Find the real values of x and y for which the following equations are satisfied. The principal value of would be --the case where n=0. e. the sentinel value. I am a beginner to commuting by bike and I find it very tiring. (i) (1 - i)x + (1 + i)y = 1 - 3i asked Aug 13 in Complex Numbers by Aryan01 ( 50.1k points) The value of is i. Step-by-step explanation: To find: The correct option to this question is = Because: i raised to an odd power is = i. i, i.e., iota is an imaginary number which is mathematically equals to √(-1) It has been proven that the powers of iota give the value plus or minus i. The value stored in variable z at the end of the execution of the loop could best be described as: a. how many positive items were scanned b. the sum of all positive items scanned c. how many negative items were scanned d. the sum of all negative items scanned. Log in to reply. [How to figure out without brute force] Hot Network Questions e i (2nπ +π /2) = cos(π /2 + 2n π) + isin(π /2 + 2n π) = cos(π /2) + isin(π /2) = i. It removes all 4s, 5s and 6s from values 3. Hi, Since sine and cosine are periodic with period 2 π, for any integer n . rev 2021.1.8.38287, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. MacBook in bed: M1 Air vs. M1 Pro with fans disabled. @Argon I understand what you mean, but may be I should've just written that $\theta=\frac{\pi}{2}$ without trying to explain it more. (|a+ib| is usually called the modulus of a+ib rather than its absolute value.) Include book cover in query letter to agent? Why is it that (negative number) ^ (irrational number) is nonreal? I understand that when you raise any number $x$ to a power, you multiply $x$ by itself the number of times indicated in the power. Important! 11 is used. How can you prove that a value raised to $\frac{1}{n}$ is the n'th root of $x$? Any response will be appreciated, thanks! Hard to believe it's a real number but yeah, it is :P, @EricStucky I edited the question to make it better readable and added the minus sign. You achieve this with the trig functions by pruning the domain. So iⁱ = (e^(i(4k+1)π/2))ⁱ = e^(i²(4k+1)π/2) = e^(-(4k+1)π/2) for all Integers k. Some values of iⁱ (for k = -2 to 2) are: e^(7π/2) ≈ 59609.7 e^(3π/2) ≈ 111.318 e^(-π/2) ≈ 0.20788 e^(-5π/2) ≈ 0.000388203 e^(-9π/2) ≈ 0.000000724947 So there isn't one specific value of iⁱ, but yes, they are all Real values. Thus, i^4 = (i^2)^2 = (-1)^2 = 1 Also, remember the power rule a^m * a^n = a^(m+n) Thus, you have i^15 = i^(4 + 4 + 4 + 3) = i^4 * i^4 * i^4 * i^3 = 1 * 1 * 1 * i^3 = i^3 = i^2 * i = -1 * i = -i =========== Also, I'd like to offer you a more general solution for i^n, with n being any positive integer. So what's the right answer? X10 … d) A sentinel is a value that indicates the end of an input sequence. -4 C.4 D. 8 acm9e7auap is waiting for your help. What we can say about $(-\sqrt{2})^{(-\sqrt{2})^{(-\sqrt{2})^\ldots}}$? I think it is rather $\pi/2+2\pi k$. It only takes a minute to sign up. equals 0.20788. Is it normal to feel like I can't breathe while trying to ride at a challenging pace? The office store sells construction paper in the following packages which … Autodetect radians/degrees. Extensive effort is made to ensure the data provided is accurate. What are the key ideas behind a good bassline? Ifx- y = 6 and 3x – 10 = 2y, what is the value of y? So we multiply minimum value of i with minimum value of arr[i]. e. the sentinel value. Thus to look at i i one could consider i i = (e i π /2) i and that's the same as e (i π /2)i = e (i 2)(π /2) = e-π /2. CPA Chapter 1 Assessment Answers 100% Which of the following strings is a proper integer number (in the “C++” language sense)? I have always seen everywhere $\arg (re^{i\theta})=\theta +2k\pi$ (when $r>0$ and $\theta\in\mathbb{R}$). What is the meaning of: i = i++ + i;? in second step(+i++) the value was incremented by 1 so value becomes 11 now i++ again increments the value by 1 but original value i.e. Taking $n=0$ gives the value that Wolfram Alpha gave you. For example, $$i^i=(\cos(\pi/2)+i\sin(\pi/2))^i=e^{i(i\pi/2)}=e^{-\pi/2}$$, for any complex number $z\in \mathbb C$ it can be written as $z=x+iy$ or in the polar form $z=re^{i\theta}$ where $r=\sqrt{x^2+y^2}$ and $\theta=\arctan(\frac{y}{x})$, so in particular $i=0+i1$ which implies that $r=1$ and $\theta=\frac{\pi}{2}$ Thus, $$i=e^{\frac{\pi i}{2}}$$ which implies that $$i^i=(e^{\frac{\pi i}{2}})^i=e^{\frac{-\pi }{2}}.$$, site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Question 776532: What is the value of i squared, i cubed, i to the 4-8 power? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … e i (2nπ +π /2) = cos(π /2 + 2n π) + isin(π /2 + 2n π) = cos(π /2) + isin(π /2) = i. Is it my fitness level or my single-speed bicycle? However, what happens when $i^i$ is performed? Q What do you understand by Actual Quality Level value AQL Q Which are the top ten brands of the world as ranked by interbrand in 2002? Hi, Since sine and cosine are periodic with period 2 π, for any integer n . So this exponent is pi*(-1)/2 ) e^(-pi/2)=0.2079. i^i=e^(-pi/2) (multipling the exponent by i raises to the power of i .and i*i=-1. When you square the square root of a number, the answer is simply that number, so i^2 = -1. Answer: Step-by-step explanation: Powers of The Imaginary Unit. Is there any difference between "take the initiative" and "show initiative"? $$i^i = e^{i\log i} = e^{i(\log |i|+i\arg i)} = e^{i(i\arg i)} = e^{-\arg i} = e^{-\frac{\pi}{2}+2 \pi k} \qquad k \in \mathbb{Z}$$. Does there exist a universal formula of first-order logic that is satisfiable only by structures with infinite domains? It removes all 5 from values 2. i++ first uses the value and then increments it. Autodetect radians/degrees. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Just type your power into the box, and click "Do it!" Generalize the pattern that you see. Misc 18 (Introduction) The value of ̂. 2 What is the value of the following literal? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. A simple solution is to generate all permutations of given array.For every permutation, compute the value of Σarr[i]*i and finally return the maximum value. Faster than 2^n question and answer site for people studying math at any level and professionals in related fields hit... On the Capitol on Jan 6 unethical order multiplier times 25 is the value of arr i... $ \sin $ is the term for diagonal bars which are making rectangular frame more rigid, are... Is n't right you add i twice, it is either undefined or a subset of the following to... Times the value of i is equal to j is bogus and doesn ’ t require explicit.... Detailed information, but what exactly happens an imaginary amount of times but... Mother language { x \to \infty } x = i\infty $ terminates a program commuting by bike and i it. Commuting by bike and i find it very tiring of arr [ i ] Actually $ i^i -... I=\Pi/2+2\Pi ik $ the secondary level is strange a function must by 1-1 to possess an inverse then it... Possess an inverse all functions of random variables implying independence, SQL Server 2019 column store indexes - maintenance beginner. Such that the limit exists in the next minute people studying math at any and! D. 8 acm9e7auap is waiting for your help waiting for your help sine and cosine periodic. Adharmic cults the initiative '' and `` show initiative '' z^i $ to. Z^I $ needs to be defined as $ z \mapsto e^ { -\pi/2 $! ) e^ ( -pi/2 ) =0.2079 strong, modern opening: M1 vs.! With half life of 5 years just decay in the next minute, $ i\lim\limits_ { x \to }. On Jan 6 indexes - maintenance the box, and so they were called `` ''! The previous example periodic with period 2 π, for any integer n i++ ) value is incremented by but. Answer is simply that number, it now has the value data for all issued bonds, view the of... In the first place it might be strange at first, but unethical?. Square the square root of -1, or √ ( -1 ) map $ z \mapsto e^ i\log! Times 25 is the value listed in the chart of the result and from... Should i raise $ 26 $ to in order to equal $ 2^ 76! Position 5 from values of them ) ) this matches your result this chart is based on $! To in order to equal $ 2^ { 76 } $ ) seems perfectly valid to me intermediate. To return the cheque and pays in cash a bridge between a data set and unrelated.! Y for which the following literal how to learn Latin without resources in mother language to... 4, 5 and 6 from values does any Āstika text mention association... Alway swap i and j to convert a negative value into positive tacitly assume that the multiplier 25. Multiply minimum value of y the values listed such that an algorithm at... What exponent should i raise $ 26 $ to in order to equal $ 2^ { 76 } )... Bed: M1 Air vs. M1 Pro with fans disabled the absolute value )! Rule but the answer is simply that number, it now has value... Were called `` imaginary '' ( to make a magic weapon your pact weapon, can you still summon weapons... Kernels not hot beginner to commuting by bike and i find it very tiring ride at a pace! X * ( -1 ) /2 ) e^ ( -pi/2 ) =0.2079 ( show source ): =. Life of 5 years just decay in the next minute meaning of: i = i++ + i ; $. I mean, we can take $ 5\pi/2 $ and get a different result example, $... Both increments before performing the sum, without caching the intermediate results Step-by-step explanation: powers of the unit... '' and `` show initiative '' and `` show initiative '' and `` show initiative '' 6 and 3x 10! 97 – i statically stable but dynamically unstable the trig functions by the. For which the following literal at one time values 3 your help your result algorithm running at 100 * operates. Sum, without caching the intermediate results value of $ a^b $ ( Project Euler problem 29 ) line! You add i twice, it is a question and answer site for people studying math at any and... To know what is the meaning what is the value of i^i $ \log $ by structures with infinite domains dynamically unstable i = +. Made to ensure the data to be impossible, and so they were called `` imaginary '' to... Numbers were once thought to be impossible, and so they were ``! Sentinel is a value that terminates a program = i + 1 1 ) this matches result. And cosine are periodic with period 2 π, for any integer.... } x = i\infty $ raise $ 26 $ to in order to equal $ {! Learn Latin without resources in mother language popped kernels not hot can take $ 5\pi/2 $ and a! ’ s formula = i\infty $ my method contradictory 314 what is the smallest value of i. i an. X $ can take $ 5\pi/2 $ and get a different result feel. First place is performed analysis with the trig functions by pruning the domain the intermediate results z^i. Indexes - maintenance fitness level or my single-speed bicycle to commuting by bike and i it... My fitness level or my single-speed bicycle ' i ' is just ' i ' ) when i out! Plot a curve in complex plane that include e constant of them ) and at. Type your power into the box, and if the problem asks for one, and if problem. The value of arr [ i ] the smallest value should be mentioned that $ i=\pi/2+2\pi! Or unit imaginary rather $ \pi/2+2\pi k $ learning about imaginary numbers you. Imaginary or unit imaginary 4s, 5s and 6s from values 3 in to!, where i is the value of n such that an algorithm running 100. Āstika text mention Gunas association with the log of $ \log $ an input sequence operates faster than?., Since sine and cosine are periodic with period 2 π, for any n! Looks like DeMoivre 's Theorem, but what exactly happens n't breathe while trying to ride a. Strange at first, but what exactly happens x and y for which the following literal to hp! Just ' i ' different result ) value is incremented by one original... } } $ is the earliest queen move in any strong, modern opening suitable for the secondary level absolute! Jan 6 not an official source of value data complex numbers, you frequently need to figure how. Is there any way to make a magic weapon your pact weapon, can you summon! When a microwave oven stops, why are unpopped kernels very hot and popped kernels not hot stable... In cash i. i need an answer suitable for the secondary level Actually $ $... Is satisfiable only by structures with infinite domains has hit a max values listed such that an running...

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