Complex Analysis: Theory and Applications · Problem 3.2.11

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · differentiable-vs-analytic

Problem

Determine where the following functions are differentiable and where they are analytic. Explain! (a) f(z)=x3+3xy2+i(y3+3x2y)f(z) = x^3 + 3xy^2 + i(y^3 + 3x^2y). (b) f(z)=8x−x3−xy2+i(x2y+y3−8y)f(z) = 8x - x^3 - xy^2 + i(x^2y + y^3 - 8y). (c) f(z)=x2−y2+i2∣xy∣f(z) = x^2 - y^2 + i2|xy|.

Browse the problem library