Question

Express -2 in triganomic form

Answer 1

$\bf -2\implies -2+0i\implies \stackrel{a}{-2}+\stackrel{b}{0}i\quad \begin{cases} r=\sqrt{a^2+b^2}\\ r=\sqrt{(-2)^2+0^2}\\ r=2\\ ----------\\ \theta =tan^{-1}\left( \frac{b}{a} \right)\\ \theta =tan^{-1}\left( \frac{0}{-2} \right)\\ \theta =tan^{-1}(0)\\ \measuredangle \theta =0~,~\pi \end{cases}$

now, there are two possible angles for that tangent... however, let's look at our a,b components.

"a" is negative whilst "b" is positive, so is not 0 then, thus

$\bf -2+0i\implies r[cos(\theta )+i~sin(\theta )]\implies 2[cos(\pi )+i~sin(\pi )]$