Results 1 to 3 of 3

Thread: Trigonometric Form

  1. #1

    Trigonometric Form

    I have no idea how to rewrite things in trigonometric form

    "Rewrite in trigonometric form:"

    -2 + sqrt(3i)

  2. #2
    Elite Member
    Join Date
    Jan 2005
    Location
    Lexington, MA
    Posts
    5,607

    Re: Trigonometric Form

    Hello, chelseafry19!

    [tex]\text{Rewrite in trigonometric form: }\;z \;=\;-2 + \sqrt{3}\,i[/tex]

    Graph the complex number.


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

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

    [tex]\text{Note that: }\;\tan\theta \:=\:\frac{\sqrt{3}}{-2} \:=\:-\frac{\sqrt{3}}{2}[/tex]

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


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

    I'm the other of the two guys who "do" homework.

  3. #3

    Re: Trigonometric Form

    Thank you!

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •