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Math Help - complex numbers

  1. #1
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    complex numbers

    hi!

    Could someone teach me how to solve (z-i)^6 = 64?

    how do you go about finding the mod and the 6 answers for z?

    thanks!
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    hi!

    Could someone teach me how to solve (z-i)^6 = 64?
    We know that \sqrt[6]{{64}} = 2. Define \sigma _k  = 2\left[ {\exp \left( {\frac{{k\pi }}{3}i} \right)} \right],\,k = 0,1 \cdots 5

    Take note: \left( {\forall k} \right)\left[ {\left( {\sigma _k } \right)^6  = 64} \right].

    Thus the six solutions are z = \sigma _k  + i,\,\,k = 0,1 \cdots 5
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  3. #3
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    and how do i find the mod of z?
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  4. #4
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    Quote Originally Posted by alexandrabel90 View Post
    and how do i find the mod of z?
    To get the modulus you will need to express in cartesian form the solutions that have been given to you.
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