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Math Help - A few complex number problems

  1. #1
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    A few complex number problems

    Hi
    The following questions i am having trouble with:

    1) Plot the set of points in the complex plane which satisfy |z+1+j|=2

    2) Express the complex number 2+2\sqrt{3}j in the form re^{j\theta} hence obtain the cartesian form of (2+2\sqrt{3}j)^6

    This is what i have attempted:
    I found out that 2+2\sqrt{3}j = 4e^{\frac{\pi}{3}j}

    hence i make (2+2\sqrt{3}j)^6 = (4e^{\frac{\pi}{3}j})^6

    what would i do next?

    P.S
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  2. #2
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    Quote Originally Posted by Paymemoney View Post
    Hi
    The following questions i am having trouble with:

    1) Plot the set of points in the complex plane which satisfy |z+1+j|=2

    2) Express the complex number 2+2\sqrt{3}j in the form re^{j\theta} hence obtain the cartesian form of (2+2\sqrt{3}j)^6

    This is what i have attempted:
    I found out that 2+2\sqrt{3}j = 4e^{\frac{\pi}{3}j}

    hence i make (2+2\sqrt{3}j)^6 = (4e^{\frac{\pi}{3}j})^6

    what would i do next?

    P.S
    1) The relation can be written |z - (-1 - j)| = 2. Geometrically, and you should know this, this defines a circle of radius 2 and center at z = -1 - j.

    2) Use an index law to simplify the power. Then convert the resulting polar form into Cartesian form.
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  3. #3
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    thank you
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  4. #4
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    Specifically, |a- b| is the distance between points in the plane, interpreted as complex numbers. So |z- a|= r is the set of points whose distance from a is r- that is, the circle with center a and radius r.
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