Answer to Question #19761 in Complex Analysis for Rod

Question

Write f(z) = 2z^2 + 3z in the u(x,y) + iv(x,y) form

Answer 1

f(u,v) = 2(u(x,y) + iv(x,y))^2 + 3(u(x,y) +iv(x,y)) = 2u^2 + 4iuv + 2(iv)^2 + 3u + 3iv = 2u^2 + 4iuv - 2v^2 + 3u +3iv