Q. Let $R$ and $C$ denote the set of real numbers and complex numbers respectively. The function $f:C \rightarrow R$ defined by $f(z) = |z|$ is
A) One to one
B) Onto
C) Bijective
D) Neither one to one nor onto
Explanation
(d)
Given, $f:C \rightarrow R$ such that $f(z) = |z|$
We know modulus of $z$ and $\overline{z}$ have same values, so $f(z)$ has many one.
Also, $|z|$ is always non-negative real numbers, so it is not onto function.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.