"Use Euler's formula to evaluate the following and write your answer in rectangular form."(adsbygoogle = window.adsbygoogle || []).push({});

A. (2i)^{5}

B. (1+i)^{-.5}

I referred to my precal book and various websites and am still clueless. I started to work out A. but I'm not sure of anything. Here's what I did:

(2i)^{5}= 32i

On the imaginary/real plane, that forms a 90 degree angle.

[tex]\theta = \frac{\pi}{4}[/tex]

[tex]e^{i \theta } = cos \theta + isin \theta [/tex]

[tex] cos \frac{\pi}{4} = 0[/tex] & [tex]isin\frac{\pi}{4} = i [/tex]

[tex]e^ {\frac{i\pi}{4}} = i [/tex]

[tex]e^ {\frac{\pi}{4}} = ? [/tex] . . .

Whenever I don't know what I'm doing, I just mimic, and I feel like I'm mimicking incorrectly.

I would really like to know how to do this but can't figure it out on my own. Thanks in advance :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Using Euler's formula

**Physics Forums | Science Articles, Homework Help, Discussion**