Question

Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to ______.

Options

• –23

• 23

• 35

• –35

Answer 1

Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to 23.

Explanation:

We have, `(x + iy)/9 = (-2 - 1/3i)^2`

`\implies ((x + iy)/9) = [-1/3 (6 + i)]^2` 

`\implies (x + iy)/9 = 1/9 (36 + i^2 + 12i)`

= `1/9 (36 - 1 + 12i)`

`\implies (x + iy)/9 = 1/9 (35 + 12i)`

On equating real and imaginary parts, we get

x = 35 and y = 12

∴ x – y = 35 – 12 = 23