Let `z=x+i y` be a complex number where `xa n dy` are integers. Then, the area of the rectangle whose vertices are the roots of the equation `z``zbar` ^3`+ `zbar`` z^3`=350` is (a)48 (b) 32 (c) 40 (d) 80

Options

A. 48
B. 32
C. 40
D. 80

Explanation

To solve the problem, we need to find the area of the rectangle whose vertices are the roots of the equation \( z \bar{z}^3 + \bar{z} z^3 = 350 \), where \( z = x + iy \) and \( x, y \) are integers.

### Step-by-Step Solution:

1. **Rewrite the Equation**:
We start with the equation:
\[
z \bar{z}^3 + \bar{z} z^3 = 350
...