Complex numbers Times - what happens to modulus and argument

Author:
Mr Creamer
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)