If z is a complex number such that `|z - barz| +|z + barz| = 4` then find the area bounded by the locus of z.

Explanation

To solve the problem, we need to analyze the given equation involving the complex number \( z \).

### Step-by-Step Solution:

1. **Express \( z \) in terms of its real and imaginary parts**:
Let \( z = x + iy \), where \( x \) and \( y \) are real numbers. The conjugate of \( z \) is \( \bar{z} = x - iy \).

2. **Substitute \( z \) and \( \bar{z} \) into the equation**:
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