If is a complex number where and are integers.
Then, the area of the rectangle whose vertices are the roots of the equation is
Explanation for the correct option.
Step 1. Form the equations.
For a complex number , the conjugate is given as: .
Now simplify the equation .
Now, as , so sum of squares would be greater than difference of squares. So,
Step 2. Solve the equations.
Add the equations and .
Substitute in equation .
So, the coordinates of the vertices of the rectangle are .
Step 3. Find the area of the rectangle.
The length of the rectangle whose vertices are is and its breadth is .
So, the area of the rectangle is
Hence, the correct option is A.