Analytic (holomorphic) functions
General · Mathematics
Study notes
Q: Is f(z) = z² analytic? What about f(z) = |z|²? z²: f'(z) = 2z exists everywhere: ENTIRE (analytic on ℂ!)! |z|² = x²+y²: real-valued non-constant - can't be analytic! (Analytic + real-valued → constant!) z̄: fails C-R: not analytic anywhere!