1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Using Euler's formula

  1. Mar 22, 2010 #1
    "Use Euler's formula to evaluate the following and write your answer in rectangular form."
    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 :)
     
  2. jcsd
  3. Mar 22, 2010 #2

    Mentallic

    User Avatar
    Homework Helper

    Well, firstly, a 90o angle isn't [itex]\pi /4[/itex], it's [itex]\pi /2[/itex] :tongue:

    If [tex]e^{\frac{i\pi}{2}}=i[/tex]

    then [tex]2e^{\frac{i\pi}{2}}=2i[/tex]

    and [tex]\left(2e^{\frac{i\pi}{2}}\right)^5=(2i)^5[/tex]

    Can you take it from here?
     
  4. Mar 22, 2010 #3
    haha thanks, I have a habit of making dumb mistakes like that.

    I'm working it a few different ways but keep winding up with:

    [tex] \cos \theta + i \sin \theta = i [/tex]

    I've flown through all of the other problems on this stupid homework, but I've been working on this problem for about two hours and I still don't know what to do.
     
  5. Mar 22, 2010 #4

    Mentallic

    User Avatar
    Homework Helper

    You're looking at the problem in entirely the wrong way.

    You need to simplify:

    [tex]\left(2e^{\frac{i\pi}{2}}\right)^5[/tex]

    Do it like you would any other real number. What is [tex](ab^2)^3[/tex]?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook