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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


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    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


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    Homework Helper

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

    You need to simplify:


    Do it like you would any other real number. What is [tex](ab^2)^3[/tex]?
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