# Thread: Problem with Complex numbers.

1. ## Problem with Complex numbers.

I have (z^(3))+2i=0 and the second is (z^(2))-2i.z-2i=1 Pls show me the right direction with these problems,10x

2. Originally Posted by wiesmann
I have (z^(3))+2i=0 and the second is (z^(2))-2i.z-2i=1 Pls show me the right direction with these problems,10x
z^3 = -2i => z = the three cube roots of -2i. Have you been taught how to find the three cube roots of a complex number using de Moivre's Theorem?

z^2 - 2i z - 2i = 1 => (z - i)^2 = 2i. Therefore z - i = the two square roots of 2i. Have you been taught how to find the two square roots of a complex number using de Moivre's theorem?

3. Originally Posted by mr fantastic
z^3 = -2i => z = the three cube roots of -2i. Have you been taught how to find the three cube roots of a complex number using de Moivre's Theorem?

z^2 - 2i z - 2i = 1 => (z - i)^2 = 2i. Therefore z - i = the two square roots of 2i. Have you been taught how to find the two square roots of a complex number using de Moivre's theorem?
OK thanks i see it now