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Math Help - Complex Number question.

  1. #1
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    Complex Number question.

    z = i(2 - i)/(1 + 2i) - (2 - i)

    For some unknown reason, I cannot get the right answer when expressing this in polar form. To start off, I multiply the fraction by:
    (1 - 2i) / (1 - 2i)
    The fraction then calculates to 5/-3. My second step is to move into the subtraction. This leaves me with the answer:
    z = (11 - 3i) / -3
    Therefore I would like to conclude that:
    z = 11/-3 + i
    Henceforth:
    a = 11/-3
    b = 1
    Now I calculate range via:
    r = sqrt(a^2 + b^2)
    After that calculation there, I can already see that I've stuffed something up along the way. Would anyone care to enlighten me please?

    Thanks in advance,
    C. Anderson
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  2. #2
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    You wandered off immediately from the start.

    (1+2i)(1-2i) = 5 -- How did you manage 3?

    1^2 - (2i)^2 = 1 - 4i^2 = 1 - (-4) = 1 + 4 = 5
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  3. #3
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    Quote Originally Posted by Turkey View Post
    z = i(2 - i)/(1 + 2i) - (2 - i)

    For some unknown reason, I cannot get the right answer when expressing this in polar form. To start off, I multiply the fraction by:
    (1 - 2i) / (1 - 2i)
    The fraction then calculates to 5/-3. My second step is to move into the subtraction. This leaves me with the answer:
    z = (11 - 3i) / -3
    Therefore I would like to conclude that:
    z = 11/-3 + i
    Henceforth:
    a = 11/-3
    b = 1
    Now I calculate range via:
    r = sqrt(a^2 + b^2)
    After that calculation there, I can already see that I've stuffed something up along the way. Would anyone care to enlighten me please?

    Thanks in advance,
    C. Anderson
    (2 - i)/(1 + 2i) = [(2 - i)(1 - 2i)]/[(1 + 2i)(1 - 2i)] = -5i/5 = -i.

    It should be simple to do now.
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