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Complex number question

  1. Jul 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose a and b are real numbers, not both 0. Find real numbers c and d, such that

    [tex]\frac{1}{a + bi}[/tex] = [tex]c + di[/tex]

    2. Relevant equations

    I said that:

    [tex] 1 = (c + di) (a + bi) [/tex]

    [tex] 1 = (ac - bd) + (bc + ad)i [/tex]

    so if b = 0 then
    [tex]\frac{1}{a} = c + di[/tex]

    The rationale holds for if a = 0. Since this is equal to a real number 1/a can I just say that c and d are real numbers?
  2. jcsd
  3. Jul 6, 2010 #2
    You need to understand that if
    x + yj = a + bj
    x = a
    y = b

    Multiply left side by a-bj / a-bj
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