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=√(a^2+b^2)\\ r=√((-2)^2+0^2)\\ r=2\\ ----------\\ \theta =tan^(-1)\left( (b)/(a) \right)\\ \theta =tan^(-1)\left( (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 )]`