If `z_1a n dz_2` are two complex numbers such that `|z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi` , then show that `z_1,=-( z )_2dot`

Explanation

To solve the problem, we need to show that if \( z_1 \) and \( z_2 \) are two complex numbers such that \( |z_1| = |z_2| \) and \( \arg(z_1) + \arg(z_2) = \pi \), then \( z_1 = -z_2 \).

### Step-by-step Solution:

1. **Express the Complex Numbers**:
Let \( z_1 \) and \( z_2 \) be expressed in their polar forms:
\[
z_1 = r_1 e^{i \theta_1} \quad \text{and} \quad z_2 = r_2 e^{i \theta_2}
...