If z lies on the circle |z−2i|=22, then the value of arg[(z – 2)/(z + 2)] is equal to

If z lies on the circle $| z - 2 i | = 2 \sqrt{2}$ , then the value of arg[(z - 2)/(z + 2)] is equal to

A
$\frac{π}{3}$
B
$\frac{π}{4}$
C
$\frac{π}{6}$
D
$\frac{π}{2}$

Solution:

$\begin{array}{l} CA = CB = 2 \sqrt{2}, OC = 2 \\ \Rightarrow OA = OB = 2 \\ \Rightarrow A \equiv 2 + 0 i, B = - 2 + 0 i \end{array}$

Clearly,

$\begin{array}{l} ∠ BCA = π / 2 \\ \Rightarrow ∠ BPA = π / 4 \\ \Rightarrow \arg (\frac{z - 2}{z + 2}) = \frac{π}{4} \end{array}$

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