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## AmTran_Bus one year ago Find the real and imaginary parts of this

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1. AmTran_Bus

|dw:1440206784952:dw|

2. AmTran_Bus

$e ^{-2 +i \pi/2}$

3. AmTran_Bus

can I use Euler's formula?

4. Zarkon

yes

5. AmTran_Bus

Hum. I just don't see it though.

6. Zarkon

$\Large e ^{-2 +i \pi/2}=e ^{-2} e^{i \pi/2}$

7. AmTran_Bus

I actually have that. But can you walk me through the steps please? Like where did the sin and cos from the formula go?

8. Zarkon

$e^{i\theta}=\cos(\theta)+i\sin(\theta)$ $e^{i\pi/2}=\cos(\pi/2)+i\sin(\pi/2)$

9. AmTran_Bus

Good. There was a problem just like that I literally just worked and got that answer. But how does that carry on to this problem? I'm so sorry, I just can't see it (this is math reveiew in a p chem book).

10. Zarkon

$\Large e ^{-2 +i \pi/2}=e ^{-2} e^{i \pi/2}=e^{-2}[\cos(\pi/2)+i\sin(\pi/2)]$ $\Large=e^{-2}[0+i\times1]=e^{-2}i$

11. AmTran_Bus

Ahhhh! Duh!!!!!! Basic unit circle!

12. Zarkon

yes

13. AmTran_Bus

I owe you a million dollars. Thanks.

14. Zarkon

np

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