Given that `|z_1+z_2|^2=|z_1|^2+|z_2|^2`, prove that `z_1/z_2` is purely imaginary.

Explanation

To prove that \( \frac{z_1}{z_2} \) is purely imaginary given that \( |z_1 + z_2|^2 = |z_1|^2 + |z_2|^2 \), we can follow these steps:

### Step 1: Start with the given equation
We are given:
\[ |z_1 + z_2|^2 = |z_1|^2 + |z_2|^2 \]

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