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I'm just starting out into Complex numbers, polar and exponential form etc... I can happily convert numbers such as $\mathrm{e}^{i \pi/2}$ but I'm a little stumped with how to handle the extra + 2 which appears in $\mathrm{e}^{(2+i \pi/2)}$. Can anyone explain how to handle that $2$?

Thanks, paar

Yiorgos S. Smyrlis
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paar
  • 13

2 Answers2

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Recall that $e^{a+b}=e^a e^b$. Replace $a$ by $a$ and $b$ by $\pi/2$.

JPi
  • 4,562
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Using Euler's formula

$$e^{2+i\pi/2}=e^2e^{i\pi/2}=e^{2}\left(\cos\left(\frac\pi 2\right)+i\sin\left(\frac\pi 2\right)\right)=ie^2$$