This may help.
The system of equations
has two solutions and in complex numbers. Find .
So far I replaced z with a+bi, did some algebra (squared both equations) and ended up with these equations:
a^2 + b^2 + (4-4a)i + 4b = 23
a^2 + b^2 - 16a + 10b + (80 - 10a - 16b )i = -1
Not sure where to go from here. Thanks!
You don't really want to start by squaring. The | |'s in this case stand for the magnitude of the complex expression inside them. This isn't the same as the square of that expression.
so for example in your first equation
do the same thing for your second equation and then you can square both sides and solve the quadratic system for a and b.