Question

The modulus of a complex number in the Argand plane denotes

• A. the real part of the complex number
• B. the imaginary part of the complex number
• C. the distance of the point from the origin
• D. none of the above

Answer 1

The correct option is C the distance of the point from the origin

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

The above figure represents point $(a,b)$ where $OM=a$ and $MP=b$. Is called Argand Diagram.

$\because OMP={90}^o$

By Pythagoras theorem,

$O{P}^2=O{M}^2+M{P}^2$

$=a^2+b^2$

$⟹OP=\sqrt{a^2+b^2}$

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

$\therefore |z|=OP$

Hence, modulus represents the distance of the point from the origin.