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Math Help - complex numbers

  1. #1
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    complex numbers

    I know this isnt dealing with triangles but it is from my trig. class.
    tried to figure tis problem out on my own but cant seem to get the right answer.

    Find the indicated roots in the form a+bi.

    the fourth roots of 16.

    can you please show me how you got the answer.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mathdud View Post
    I know this isnt dealing with triangles but it is from my trig. class.
    tried to figure tis problem out on my own but cant seem to get the right answer.

    Find the indicated roots in the form a+bi.

    the fourth roots of 16.

    can you please show me how you got the answer.
    Note that 16=16\cdot 1=16\left(\cos 0+i\sin 0\right).

    When you find the fourth roots, you need to simplify \sqrt[4]{16}\left(\cos\!\left(\tfrac{2k\pi}{4}\right)+i\si  n\!\left(\tfrac{2k \pi}{4}\right)\right)=2\left(\cos\!\left(\tfrac{k\  pi}{2}\right)+i\sin\!\left(\tfrac{k\pi}{2}\right)\  right) for k=0,1,2,3.
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