If the real part of `(barz +2)/(barz-1)` is 4, then show that the locus of the point representing z in the complex plane is a circle.

Explanation

To solve the problem, we need to show that the locus of the point representing \( z \) in the complex plane is a circle, given that the real part of \( \frac{\bar{z} + 2}{\bar{z} - 1} \) is equal to 4.

Let's denote \( z \) as \( x + iy \), where \( x \) and \( y \) are real numbers, and \( \bar{z} \) (the conjugate of \( z \)) is \( x - iy \).

### Step-by-step Solution:

1. **Substituting \( z \) and \( \bar{z} \)**:
\[
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