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Math Help - Show me the steps to solving complex numbers involving e?

  1. #1
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    Show me the steps to solving complex numbers involving e?

    My teacher didn't go into too much detail on these equations and they were on a test, so I'd like to know how to solve these equations for my final.


    Z= Show me the steps to solving complex numbers involving e?-codecogseqn-1-.gif

    Can someone show me the steps how to get this complex number into algebraic form answer Z=4i ?



    Find the product of Show me the steps to solving complex numbers involving e?-codecogseqn-2-.gif and conjugate Z?

    How do I solve to get the answer 27?
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  2. #2
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    Re: Show me the steps to solving complex numbers involving e?

    Hello, INeedOfHelp!

    z \,=\,4e^{\frac{\pi}{2}i}

    Can someone show me the steps how to get this complex number into algebraic form: z 4i

    z \:=\:4e^{\frac{\pi}{2}i} \;=\;4\left(\cos\tfrac{\pi}{2} + i\sin\tfrac{\pi}{2}\right) \;=\; 4(0 + i\!\cdot\!1) \;=\;4i




    Find the product of z \,=\,3\;\!\sqrt{3}e^{\pi i} and its conjugate \overline{z}

    How do I solve to get the answer 27?

    We have: . \begin{Bmatrix}z &=& 3\sqrt{3}\;\!e^{\pi i} \\ \\[-3mm] \overline{z} &=& 3\sqrt{3}\;\!e^{-\pi i} \end{Bmatrix}

    Therefore: . z\cdot\overline{z} \;=\;\left(3\sqrt{3}\;\!e^{\pi i}\right)\left(3\sqrt{3}\;\!e^{-\pi i}\right) \;=\; \left(3\sqrt{3}\cdot3\sqrt{3}\right)\left(e^{\pi i}\cdot e^{-\pi i}\right)

    n . . . . . . . . . . . =\;(27)(e^0) \;=\;(27)(1) \;=\;27
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  3. #3
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    Re: Show me the steps to solving complex numbers involving e?

    Oh well that's easy enough, thank you very much.
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