Question

If a complex number $z$ is perfectly real, then the modulus of $z$,

• A. $|z|=z^2$
• B. $|z|=2z$
• C. $|z|=z$
• D. $|z|=-iz$

Answer 1

The correct option is C $|z|=z$

Let $z=x+iy$ be any complex number where imaginary part does not exist i.e. $y=0$ $⟹z=x$

We know that, $|z|=\sqrt{x^2+y^2}$

$⟹|z|=\sqrt{x^2+0^2}=\sqrt{x^2}=x=z$

Hence, $|z|=z$