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Math Help - Complex Number in its simplest form

  1. #1
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    Complex Number in its simplest form

    Hi all. Not sure whether this is correct or not and I would like some guidance! Thanks...

    Given that z1 = 4-j5 and z2 = -3+j4, Find the compelx number z1/z1-z2 in its simplest form.

    This is what I have...

    z1 / (z1 -z2) = (4 - j5) / (4 - j5 +3 -j4) = (4-j5)/(7 - j9)

    =[ (4-j5) x (7+j9) ] / [ (7-j9) x (7+j9) ]

    =[ (4x7 - (-5) 9) + j(4x9+(-5)x7) ] / (49+81)

    =(73+j)/130

    =73/130+j/130
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  2. #2
    Senior Member eumyang's Avatar
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    Looks right to me!
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  3. #3
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    Thanks! I really had doubts about "z1 / (z1 -z2) = (4 - j5) / (4 - j5 +3 -j4) = (4-j5)/(7 - j9)"

    I wasn't sure whether it was (4 - j5 + 3 - j4) or (4 - j5 + 3 +j4)
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    Thumbs up

    Quote Originally Posted by Benji123 View Post
    Hi all. Not sure whether this is correct or not and I would like some guidance! Thanks...

    Given that z1 = 4-j5 and z2 = -3+j4, Find the compelx number z1/z1-z2 in its simplest form.
    \frac{z1}{z1-z2}=\frac{4-5j}{4-5j-(-3+4j)}
    \frac{z1}{z1-z2}=\frac{4-5j}{4-5j+(3-4j)}
    \frac{z1}{z1-z2}=\frac{4-5j}{7-9j}


    -- hope it'll help --
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    So do I need to rationalize it or leave it as 4-5j/7-9j? Thanks.
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  6. #6
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    You rationalise it, yes. Your answer is good, do not worry
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  7. #7
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    Thanks people
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