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Math Help - Complex number solution for theta

  1. #1
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    Question Complex number solution for theta

    Given z = -1 - sqrt(3)i

    What is the value of theta?
    I got pi/3 but that is not right, the correct answer is -2pi/3

    Thanks
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  2. #2
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    Quote Originally Posted by taurus View Post
    Given z = -1 - sqrt(3)i

    What is the value of theta?
    I got pi/3 but that is not right, the correct answer is -2pi/3

    Thanks
     \frac{\pi}{3} is your reference angle

    Think of -1 as being the x coordinate and -\sqrt{3} as your y

    This you put the point in quadrant III rotated down \frac{\pi}{3} from the negative x-axis.

    I hope this helps.
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  3. #3
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    i still dont get it?
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  4. #4
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    Hello, taurus!

    Did you make a sketch?


    Given: . z \:= \:-1 - i\sqrt{3}

    What is the value of \theta ?
    Code:
                    |
                    |
                    |
                -1  |
          - - + - - * - - - -
              :    /|
            _ :   / |
          -√3 :  /  |
              : /   |
              :/    |
              *     |

    Can you see that the angle is: . \theta \;=\;240^o\,\text{ or }\,\text{-}120^o ?


    In radians: . \theta \;=\;\frac{4\pi}{3}\,\text{ or }\,\text{-}\,\frac{2\pi}{3}

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  5. #5
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    Question

    How did u get the -2pi/3?

    i did this:
    -120*pi/360
    =pi/3 which is not right?
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