Mathematics - Complex Analysis - Complex functions - Complex Function Problems

8 problems: (1-2) Decompose into u+iv: f(z)=z³, f(z)=1/z. (3-4) Verify Cauchy-Riemann for f(z)=eᶻ, f(z)=sin(z). (5) 'Show f(z)=|z|² is NOT analytic.' (6) 'Find where f(z)=z²+iz is zero.' (7) 'If f(z)=u+iv is analytic, show u and v are harmonic (∇²u=0).' (8) 'Find the Taylor series of eᶻ at z=0 (same