A complex function f(z) = u(x,y) + i v(x,y) and its complex conjugate f*(z) = u(x,y) – i v(x,y) are both analytic in the entire complex plane, where z = x + i y and i = $\sqrt{-1}$. The function f is then given by
- f(z) = x + i y
- f(z) = x$^{2}$ – y$^{2}$ + i 2xy
- f(z) = constant
- f(z) = x$^{2}$ + y$^{2}$