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Math Help - Complex no clarifications

  1. #1
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    Complex no clarifications

    Hi I have a few more doubts!

    How do I get from -((3-2i))^2 to (3i+2)^2?

    I know the - sign in front is i^2, so I multiply it in..but if I multiply i^2 in isn't it (3i^2-2i^3)^2 instead, thus (-3+2i)^2?

    Also, is |a-bi| = a+bi?

    Thank you so so much!
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  2. #2
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    Re: Complex no clarifications

    \displaystyle \begin{align*} - \left[ \pm \left( 3 - 2i \right) \right]^2 &= -\left( 3 - 2i \right)^2 \\ &= - \left( 9 - 12i - 4 \right) \\ &= - \left( 5 - 12i \right) \\ &= -5 + 12i \end{align*}

    and

    \displaystyle \begin{align*} \left( 3i + 2 \right)^2 &= -9 + 12i + 4 \\ &= -5 + 12i \\ &= - \left[ \pm \left( 3 - 2i \right) \right]^2  \end{align*}
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  3. #3
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    Re: Complex no clarifications

    Quote Originally Posted by Tutu View Post
    Hi I have a few more doubts!

    How do I get from -((3-2i))^2 to (3i+2)^2?

    I know the - sign in front is i^2, so I multiply it in..but if I multiply i^2 in isn't it (3i^2-2i^3)^2 instead, thus (-3+2i)^2?

    Also, is |a-bi| = a+bi?

    Thank you so so much!
    Surely you know that | | is a non-negative real number? So "|a- bi|= a+ bi" is automatically impossible. It possible that you meant to ask if |a- bi|= |a+ bi|. The answer to that is certainly yes: |a- bi|= \sqrt{a^2+ (-b)^2}= \sqrt{a^2+ b^2}= |a+ bi|.
    Thanks from topsquark
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