Femtobytes
Problem type

Add, subtract, multiply and divide complex numbers

What it solves
All four operations on two complex numbers, each worked from the single fact that i squared is minus one: parts added side by side, brackets multiplied out term by term, and division done by the conjugate and then checked by multiplying back.
Subject
Complex Numbers
Topic
Arithmetic with complex numbers
Also called
add complex numbers, multiply complex numbers, divide complex numbers, conjugate, rationalise the denominator
Your problem

Work out z+wz + w, z−wz - w, zwzw and zw\dfrac{z}{w}.

z=2+3i,w=1−iz = 2 + 3 i, \qquad w = 1 - i
Invent a new one: