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Homework Help: Simple Complex number

  1. Aug 11, 2011 #1
    how to solve sqrt(-8.3)sqrt(1 - i8)?

    i try to solve it.. but got the wrong answer..

    sqrt(-8.3)sqrt(1 - i8) = sqrt[(8.3i^2)(1 - 8i)]
    = sqrt (8.3i^2 - 66.4i)
    = 2.88i + 8.15

    the answer should be.. 5.41 + i6.13
  2. jcsd
  3. Aug 11, 2011 #2


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    Homework Helper

    Here's a problem (in bold). You can't take the square root of a sum/difference separately. In other words,
    [itex]\sqrt{a + b} \ne \sqrt{a} + \sqrt{b}[/itex]
  4. Aug 11, 2011 #3
    then... what should i do..? i got stuck there...
  5. Aug 11, 2011 #4


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    Assuming you want just the principal square root, consider this: if there is a complex number a + bi such that
    [itex]\sqrt{z} = a + bi[/itex],
    then it makes sense that
    [itex]z = (a + bi)^2[/itex].

    First simplify the expression so that there is one square root. You sort of did that here (in bold):
    ... but there is a sign mistake. Also, forget about rewriting a negative as i2 in your 1st step.

    Whatever is under the square root is your z. Take this:
    [itex]z = (a + bi)^2[/itex]
    and expand the right-hand side. Equate the real number parts and the imaginary number parts. You'll end up with 2 equations and 2 unknowns. Solve for a and b.
    Last edited: Aug 11, 2011
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