When solving for the value, we know that $e^{\pi i}=-1$ . I am confused as to what is the right answer when you evaluate this.I am getting two possible answers: $e^{3\pi i/2}$ = $(e^{\pi i})^{3/2}$ so this could be $(\sqrt{-1})^3=i^3=-i$ or it could be $\sqrt{(-1)^3}=\sqrt{-1}=i$. Which one is the correct answer, and where am I going wrong? Thanks.
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https://math.stackexchange.com/questions/37560/intuition-behind-eulers-formula – lab bhattacharjee May 17 '19 at 18:58
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3In the complex world, exponents do not behave the same as in the so-called "real" world. – The Count May 17 '19 at 18:59
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2This is a similar error to believing that $(\sqrt{-1})^2 = \sqrt{(-1)^2}$. In general $a^{bc}=(a^b)^c$ will be true for positive real values of $a$ and real exponents, but as soon as you let $a$ be negative or let $b,c$ be nonreal things can break. – JMoravitz May 17 '19 at 19:02
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Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. – dantopa May 18 '19 at 15:17
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$$e^{3\pi i/2}:=\cos\frac{3\pi}2+i\sin\frac{3\pi}2=0+i\cdot(-1)=-i$$
DonAntonio
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