Answer to Question #103627 in Algebra for na

Question

For any z∈C, if |z| , then ∈R z∈ R . Is it true or false ? Give reasons.

Answer 1

Let $z=a+bi \in \mathbb{C},$ then $\left|z\right| = \sqrt{a^2+b^2}$. Therefore, the absolute value of a complex number always lies in $\mathbb{R}.$

Answer: False.