`Z_1!=Z_2` are two points in an Argand plane. If `a|Z_1|=b|Z_2|,` then prove that `(a Z_1-b Z_2)/(a Z_1+b Z_2)` is purely imaginary.

Explanation

To prove that \(\frac{a Z_1 - b Z_2}{a Z_1 + b Z_2}\) is purely imaginary given that \(a |Z_1| = b |Z_2|\) and \(Z_1 \neq Z_2\), we can follow these steps:

### Step 1: Express \(Z_1\) and \(Z_2\) in polar form
Let:
\[ Z_1 = r_1 e^{i\theta_1} \]
\[
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