Trigonometric Form

chelseafry19

New member
Joined
Mar 10, 2010
Messages
2
I have no idea how to rewrite things in trigonometric form

"Rewrite in trigonometric form:"

-2 + sqrt(3i)
 
Hello, chelseafry19!

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

Graph the complex number.


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

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

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

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


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

 
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