Question

w=f(z)=|z|^2-----------is it a continuity function or not?what is the derivative of this function? (z=complex number)---(Medal!)

Answer 1

@FutureMathProfessor

Answer 2

The continuity part is easy...for the derivative use the Cauchy–Riemann equations

Answer 3

Suppose z = x + i y
then
\[
f(z)=|z|^2= x^2 +y^2 + 0 i
\]
f takes only real values. Can be it be analytic?