Mathematics - Complex Analysis - Complex functions - Analytic Functions

10 steps: (1) A complex function f:ℂ→ℂ maps complex numbers to complex numbers. (2) f(z)=z² maps a+bi to (a²-b²)+2abi. (3) ANALYTIC (holomorphic): f has a complex derivative at every point in a region. (4) CAUCHY-RIEMANN EQUATIONS: if f=u+iv, then ∂u/∂x=∂v/∂y and ∂u/∂y=-∂v/∂x. (5) These are the test