MAT3705 ASSIGNMENT 2 2026 – FULLY ANSWERED (DUE 4 JUNE 2026)

Description

MAT3705 Assignment 2 Memo | Due 4 June 2026. All questions fully answered. 1. Let f(z) =
iz
|z|2 . The aim of this question is to determine where f is differentiable using the Cauchy-
Riemann equations. It is advisable that you work through the problem in detail before completing the table
above (in other words, work through the problem as you normally would and then select the appropriate
options to enter into the table). Please note that only the completed table will be marked in this section.
(a) Select which option below provides the correct expressions for u and v when we write f = u+iv, with
u and v being real-valued functions:
i. u(x, y) =
x
x2 + y2 and v(x, y) =
y
x2 + y2
ii. u(x, y) =
y
x2 + y2 and v(x, y) =
x
x2 + y2