Find all complex numbers z, which satisfy z^(2)= i - 1.

I have come across this question during my tutorial and I cant seem to solve it. I need some reference. Thank you---> to the kind soul who is able to help me out here... =D

God Bless.

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- Dec 8th 2010, 08:57 PMsaykhongSolving Complex Numbers.
Find all complex numbers z, which satisfy z^(2)= i - 1.

I have come across this question during my tutorial and I cant seem to solve it. I need some reference. Thank you---> to the kind soul who is able to help me out here... =D

God Bless. - Dec 8th 2010, 09:19 PMdwsmith

- Dec 8th 2010, 09:26 PMProve It
Exponential equations are easiest to solve when you put the complex numbers in exponential form. Remember that the are always 2 square roots, 3 cube roots, 4 fourth roots, etc, and they are all evenly spaced around a circle.

So for square roots, they are separated by an angle of .

Anyway, .

.

So that means .

Therefore,

.

That is the first square root. The second has an extra added to its angle. So the other square root is

. - Dec 8th 2010, 09:58 PMsaykhong
That was really some good help. And please keep the spirit up high in this forum! Its because of people like that people like us continue to learn everyday!