Question

Express the complex number in trigonometric form. square root of 3+2i

Answer 1

$\bf \begin{array}{llll} \sqrt{3}&,&2i\\ \uparrow &&\uparrow \\ a&&b \end{array}\implies r[cos(\theta )+i\ sin(\theta )]\qquad \begin{cases} r=\sqrt{a^2+b^2}\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases} \\\\\\ r=\sqrt{(\sqrt{3})^2+(2)^2}\implies r=\sqrt{3+4}\implies r=\sqrt{7} \\\\\\ \theta =tan^{-1}\left( \frac{2}{\sqrt{3}} \right)\implies \theta \approx 49.10660535^o\textit{ or just 49 rounded up}\\\\ -------------------------------\\\\ \sqrt{3},2i\implies \sqrt{7}[cos(49^o)+i\ sin(49^o)]$