Given question :
$x+iy = tan(u+iv)$ where $x, y, u, v$ are all real, prove that the curves u = constant give a family of coaxal circles passing through the point $(0, 1)$ and $(0, -1)$ and that the curves v = constant give a system of circles cutting the first given system orthogonally
I don't seem to understand what this question wants to ask. I am only a beginner in complex numbers and I know how to find the tan of a complex number. I thought I may need to equate the real and imaginary parts of both sides and then find a relation between x and y but how do I then deal with the sinh and cosh. It seems too complicated that way.