If `2z_1//3z_2` is a purely imaginary number, then find the value of `"|"(z_1-z_2")"//(z_1+z_2)|dot`

Explanation

To solve the problem, we need to find the value of \(|\frac{z_1 - z_2}{z_1 + z_2}|\) given that \(\frac{2z_1}{3z_2}\) is a purely imaginary number.

### Step-by-Step Solution:

1. **Understanding the Given Condition**:
We are given that \(\frac{2z_1}{3z_2}\) is purely imaginary. This means that the real part of \(\frac{2z_1}{3z_2}\) is zero.

2. **Expressing the Condition**:
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