If `|z-5i|=|z+5i|` , then the locus of `zdot`

Explanation

To solve the problem, we need to find the locus of the complex number \( z \) given that \( |z - 5i| = |z + 5i| \).

### Step-by-Step Solution:

1. **Express \( z \) in terms of its real and imaginary parts**:
Let \( z = x + yi \), where \( x \) and \( y \) are real numbers.

2. **Substitute \( z \) into the given equation**:
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