1. Let z1 be on on the vertical axis (0+1i) and move z2 around. What do you notice?
2. Change the modulus (length) of z1 to 2 so it now becomes 0+2i. What do you notice? Keep changing the modulus of z1 and observe what happens to z1 x z2

Extra

What happens if you let z1 be 1+1i so it forms a 45° angle to the horizontal axes. Move z2 around. What do you notice?