2014-12.md

course	course_year	question_number	tags	title	year
Complex Methods	IB	12	IB 2014 Complex Methods	Paper 3, Section I, B	2014

Find the most general cubic form

$$u(x, y)=a x^{3}+b x^{2} y+c x y^{2}+d y^{3}$$

which satisfies Laplace's equation, where $a, b, c$ and $d$ are all real. Hence find an analytic function $f(z)=f(x+i y)$ which has such a $u$ as its real part.