Question

Represent the complex number $3+4i$ on an Argand plane. The modulus is:

Answer 1

Let $z=a+ib=3+4i$

$⟹|z|=\sqrt{a^2+b^2}$ ..... (1)

From the above figure,

$△OPM={90}^o$, $OM=3=a,MP=4=b$

By Pythagoras theorem,

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

$=3^2+4^2=25=a^2+b^2$

$\therefore OP=5=\sqrt{a^2+b^2}$ ........ (2)

Form (1) and (2)

$|z|=5$

Hence, $|3+4i|=5$.