Question

If \(|Z|\le 1\), \(|W| \le 1\), Show that \[|Z-W|^2 \le (|Z| - |W|)^2 + (\text{arg} Z - \text{arg} W)^2)\]
\(Z \text{ and } W\) are Complex Numbers.

Answer 1

ahhh,very displeasing to eyes

Answer 2

i know, that is why i didn't try it :-D

Answer 3

Why did you capital letters? It makes it look not good.

Answer 4

idk maybe because it;s the same notation used in my book

Answer 5

Let \(\large z=r_1e^{i\theta_1}\) and \(\large w=r_2e^{i\theta_2}\), then we're asked to show
\[|r_1e^{i\theta_1}-r_2e^{i\theta_2}|^2\le (r_1-r_2)^2+(\theta_1-\theta_2)^2.\]

Answer 6

For the geometers out there, start with the Cosine Law