# Complex numbers Times - what happens to modulus and argument

- Author:
- Mr Creamer

- Topic:
- Complex Numbers, Numbers

z' = wz
You can move w and z around to see what happens.
Experiment then try to answer the questions below
Note to change to a polar grid select the arrow tool at the top left, click the grid too at top right and then select the polar choice (3rd)

Q1

**Modulus**Look at the modulis of w, z and z' What is the relationship between mod(w) and mod(z) with mod(z')? Can you write out a rule using these 3 numbers? Q2**Angles / Arguments**The argument of z is θ The argument of w is φ What is the argument of z' in terms of θ and φ ? Can you write out a rule for complex multiplication for arg(w), arg(z) and arg(wz)