Question

If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.

Options

• 10

• 8

• –9

• –10

Answer 1

If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to 10.

Explanation:

`(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0

Let z = x + iy

⇒ (3 + i)(2x) – (2 + i)(2iy) + 14i = 0

⇒ (3 + i)x – (2 + i)iy + 7i = 0

⇒ (3x + y) + (x – 2y + 7)i = 0

⇒ 3x + y = 0 and x – 2y + 7 = 0

Solving we get x = –1, y = 3

`zbarz` = x² + y² = 1 + 9 = 10