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Math Help - Solving a power of a complex number

  1. #1
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    Solving a power of a complex number

    I have this problem:

    x^4=4-4*(square root 3i)

    I rewrote in trig form:

    8cos300+isin300 then i solved by raising the 8^4 and multiplying the angle by 4...

    The answer i got was 1499i. Could anyone verify my work for me? Is it correct to leave the imaginary "i" in the answer?
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  2. #2
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    Quote Originally Posted by nascar77 View Post
    I have this problem:

    x^4=4-4*(square root 3i)

    I rewrote in trig form:

    8cos300+isin300 then i solved by raising the 8^4 and multiplying the angle by 4...

    The answer i got was 1499i. Could anyone verify my work for me? Is it correct to leave the imaginary "i" in the answer?
    There are four solutions, found by raising  8 \cos (300 + 360n) + i \sin (300 + 360n) to the power of 1/4, where n is an integer. Using four consecutive values of n (such as n = 0, 1, 2 and 3) after doing this will give you the four solutions.
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