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Math Help - Complex Number division

  1. #1
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    Complex Number division

    Given w=2-3i and z=4+3i

    How do i calculate:
    (w+z)/(w-z)?

    I thought addition top line and subtraction bottom line then divide but that did not give the right answer?
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  2. #2
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    Hello, taurus!

    Given: . w\:=\:2-3i\,\text{ and }\,z\:=\:4+3i

    Find: . \frac{w+z}{w-z}

    We have: . \begin{array}{ccccc}w + z &=& (2-3i) + (4+3i) &=& 6 \\ w-z & = & (2-3i) - (4+3i) &=& -2 - 6i\end{array}

    . . Then: . \frac{w+z}{w-z} \;=\;\frac{6}{-2-6i} \;=\;\frac{6}{-2(1 + 3i)} \;=\;\frac{-3}{1 + 3i}

    Rationalize: . \frac{-3}{1+3i}\cdot\frac{1-3i}{1-3i} \;=\;\frac{-3(1-3i)}{1 - 9i^2} \;=\;\frac{-3(1-3i)}{10}


    Answer: . -\frac{3}{10} + \frac{9}{10}i

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  3. #3
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    How did u get 6, i got 6+1i?


    thanks
    Last edited by taurus; June 6th 2008 at 11:31 AM.
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  4. #4
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    Question

    Why did the 1i dissappear?
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  5. #5
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    How did you get that? 3i - 3i = 0 \neq i There never was an 'i', so how could it have disappeared?
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