z+z 0, if and only if - Vidyadip

MCQ

$z+\bar{z} \neq 0$, if and only if

✓
$\operatorname{Re}(z) \neq 0$
B
$\operatorname{Im}(z) \neq 0$
C
$z \neq 0$
D
$|z| \neq 0$

✓

Answer

Correct option: A.

$\operatorname{Re}(z) \neq 0$

(A)
$z+\bar{z} \neq 0$
$\Rightarrow x+ i y+x- i y \neq 0$
$\Rightarrow x \neq 0$
$\Rightarrow \operatorname{Re}( z ) \neq 0$

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