Let z be a complex number satisfying `|z| = 3 |z-1|`. Then prove that `|z-(9)/(8)| = (3)/(8)`

Explanation

To solve the problem, we need to prove that if \( |z| = 3 |z - 1| \), then \( |z - \frac{9}{8}| = \frac{3}{8} \).

### Step-by-Step Solution:

1. **Let \( z = x + iy \)**:
We start by expressing the complex number \( z \) in terms of its real and imaginary parts, where \( x \) is the real part and \( y \) is the imaginary part.

2. **Use the modulus condition**:
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