Example 1.2.14 (d): Multiplying geometrically
Compute in your head, then confirm your answer.
To do this in our head we look at radius and angle separately:
According to our results on multiplying and dividing geometrically we have for the lengths:
length of = (1)/() = 1
As for the angles we have:
angle of = /2 + /4 + 3/4 - 2(-/4) = 2
= 1 cis(2) = 1
Verifying this algebraically is work - so it's left to you.