Question

The modulus of a complex number is

• A. always positive
• B. always negative
• C. may be positive or negative
• D. $0$

Answer 1

The correct option is A always positive

Let $z=a+ib$ be any complex number, where $a$ and $b$ are real numbers.

$⟹|z|=\sqrt{a^2+b^2}$

We know that $x^2>0$, for every real number

$⟹a^2,b^2>0$

$⟹a^2+b^2>0$

$⟹\sqrt{a^2+b^2}>0$

$\therefore |z|>0$

Hence, modulus of complex number is always positive.