Question

Find the modulus and argument of $\sqrt{3}+\sqrt{2}i$.

Answer 1

Given,

$z=\sqrt{3}+i\sqrt{2}$

modulus $|z|=\sqrt{(\sqrt{3}{)}^2+(\sqrt{2}{)}^2}=\sqrt{5}$

argument $\theta ={\tan }^{-1}\left(\frac{\sqrt{2}}{\sqrt{3}}\right)\Rightarrow \theta ={39.23}^{\circ }$