# Thread: Complex Numbers,

1. ## 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!!

2. 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...