If `za n dw` are two complex number such that `|z w|=1a n da rg(z)-a rg(w)=pi/2` , then show that ` z w=-idot`

Explanation

To solve the problem, we need to show that if \( z \) and \( w \) are two complex numbers such that \( |zw| = 1 \) and \( \arg(z) - \arg(w) = \frac{\pi}{2} \), then \( z \overline{w} = -i \).

### Step-by-Step Solution:

1. **Express \( z \) and \( w \) in Euler's form**:
Let \( z = r_1 e^{i\theta_1} \) and \( w = r_2 e^{i\theta_2} \), where \( r_1 = |z| \), \( r_2 = |w| \), \( \theta_1 = \arg(z) \), and \( \theta_2 = \arg(w) \).

2. **Use the modulus condition**:
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