Question

Is The Modulus of A Complex Number Always Positive?

Answer 1

Considering an example to prove that the modulus of a complex number is always positive:

Let $z=a+ib$ be a complex number.

Taking modulus

$\left|z\right|=\sqrt{a^2+b^2}$

We know $x^2$ will be greater than zero.

Therefore, $$\begin{gathered} \Rightarrow a^2,b^2>0 \\ \Rightarrow a^2+b^2>0 \\ \Rightarrow \sqrt{a^2+b^2}>0 \end{gathered}$$

Thus, $\left|z\right|>0$

Therefore, The Modulus of A Complex Number is Always Positive.