Question

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

Answer 1

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