We know that two complex numbers are equal if their imaginary part and real part are equal from that we get this system of equation. $$\begin{cases} x²-y² =a \\ x²+y² =\sqrt{a²+b²}\\ 2xy=b \end{cases}$$
I tried to isolate one variable at a time with no success. I tried to substitute $x² +y² = 2y² +a $ into second equation in the system then square both sides I ended up with a messy equality.
So my question is what's approach/trick I needed here to solve this?
