1. ## Trigonometric Form

I have no idea how to rewrite things in trigonometric form

"Rewrite in trigonometric form:"

-2 + sqrt(3i)

2. ## Re: Trigonometric Form

Hello, chelseafry19!

$\text{Rewrite in trigonometric form: }\;z \;=\;-2 + \sqrt{3}\,i$

Graph the complex number.

Code:
        *         |
: *       |
_ :   *     |
/3 :     *
:       * @
- - - + - - - - + - - - -
-2    |

$\text{The hypotenuse is: }\:r^2 \:=\-2)^2 + (\sqrt{3})^2 \:=\:4+3 \:=\:7 \quad\Rightarrow\quad r \:=\:\sqrt{7}$

$\text{Note that: }\;\tan\theta \:=\:\frac{\sqrt{3}}{-2} \:=\:-\frac{\sqrt{3}}{2}$

. . $\text{Hence: }\:\theta \:=\:\arctan\left(-\frac{\sqrt{3}}{2}\right)\:\text{where }\theta\text{ is in Quadrant 2.}$

$\text{Therefore: }\;z \;=\;\sqrt{7}\,\bigg(\cos\theta + i\sin\theta\bigg)$

3. ## Re: Trigonometric Form

Thank you!

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