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Math Help - Complex Numbers,

  1. #1
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    Complex Numbers,

    Find the complex number z=a+bi such that z^3 = 2+2i where a is smaller or equal to zero and b is greater or equal to zero.

    Find the values of all of the following:
    (1-sqrt(3)i)^(1/3)

    (i+1)^(1/2)


    Thanks in advance!!
    Last edited by eiktmywib; December 6th 2008 at 06:58 PM.
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  2. #2
    Member Mentia's Avatar
    Joined
    Dec 2008
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    Bellingham, WA
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    134
    I assume you are using the equation:

     \sqrt[ n]{ z} =  \sqrt[ n]{ r} \left (cos \left (  \frac{ \theta + 2k \pi  }{ n}   \right )  +  isin \left (  \frac{  \theta + 2k \pi }{n }   \right )   \right )

    In this case theta is pi/4, n is 3, r is 8^(1/2)

    plug in each of k = 0, 1, 2

    and see what happens. It looks like you may have done this already though...
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