Complex numbers equation

[mathwannabe]

Hello everybody

I had no idea where to put this thread so I took the risk and placed it in "Beginning Algebra". Sorry If I made a mistake.

I started working with complex numbers, but I ran into a problem I have no idea how to solve.

It says:

1) Find all solutions in the set of complex numbers for the equation: conjugate z = z^2

as I said, I have no idea how to solve this. I tried like:

x - yi = (x + yi)^2

x - yi = x^2 +2xyi -y^2

x - yi = (x - y)(x + y) + 2xyi

but that leads me to nowhere.

Any hints?

 

[Oaky]

LaTeX is completely screwing up, so might be slightly difficult to read...

a - bi = (a + bi)^2
a - bi = a^2 + 2abi - b^2
a - a^2 + b^2 - bi - 2abi = 0
(a - a^2 + b^2) - (b + 2ab)i = 0 + 0i, because a and b are real numbers

therefore you get two simultaneous equations
a - a^2 + b^2 = 0
-b - 2ab = 0

Should be able to get the rest of the way on your own

 

[mathwannabe]

LaTeX is completely screwing up, so might be slightly difficult to read...

a - bi = (a + bi)^2
a - bi = a^2 + 2abi - b^2
a - a^2 + b^2 - bi - 2abi = 0
(a - a^2 + b^2) - (b + 2ab)i = 0 + 0i, because a and b are real numbers --- This is what I couldn't have figured out on my own.

therefore you get two simultaneous equations
a - a^2 + b^2 = 0
-b - 2ab = 0

Should be able to get the rest of the way on your own

Yes, thank you.