Question

If z is the complex number. Which of the following is/are true?

• A. zz ̅ = |z|²
• B. z + z ̅ = 2Re (z)
• C. z - z ̅ = 2Im (z)
• D. All of these

Answer 1

The correct option is D

All of these

Let z = x +iy

$\overline{z}$ = x - iy

Option A : $z.\overline{z}$ = (x + iy) (x - iy) = $x^2$ + $y^2$ = $|z{|}^2$ Correct

Option B : $z+\overline{z}$ = x + iy + x - iy = 2x = 2Re (z) Correct

Option C : $z-\overline{z}$ = x + iy - x + iy = 2yi = 2lm (z) Correct

So, all the above given options are correct.