Question

Find modulas $(1+\sqrt{3})+i(1-\sqrt{3})$

Answer 1

$z=x+iy$

modulus of z:

$|z|=\sqrt{x^2+y^2}$

Given,

$z=(1+\sqrt{3})+i(1-\sqrt{3})$

$|z|=\sqrt{(1+\sqrt{3}{)}^2+(1-\sqrt{3}{)}^2}$

$=\sqrt{1+3+2\sqrt{3}+1+3-2\sqrt{3}}$

$=\sqrt{8}=2\sqrt{2}$

Modulus of $(1+\sqrt{3})+i(1-\sqrt{3})=2\sqrt{2}$