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Math Help - the right question

  1. #1
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    the right question

    write in rectangular form

    (square root 2-i) 4th power
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  2. #2
    Forum Admin topsquark's Avatar
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    \left ( \sqrt{2-i} \right )^4

    = (2-i)^2 = 4 - 4i + i^2 = 4 - 4i - 1 = 3 - 4i

    -Dan
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  3. #3
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    Hello, Shorty!

    Is this what you meant?


    Write in rectangular form: (\sqrt{2} - i)^4

    Just expand it . . . what's stopping you?

    (\sqrt{2} - i)^4 \;=\;(\sqrt{2})^4 - 4(\sqrt{2})^3(i) + 6(\sqrt{2})^2(i^2) - 4(\sqrt{2})(i^3) + (i^4)

    . . . . . . . = \;16 - 4(2\sqrt{2})(i) + 6(2)(-1) - 4(\sqrt{2})(-i) + 1

    . . . . . . . = \;16 - 8\sqrt{2}i - 12 + 4\sqrt{2}i + 1

    . . . . . . . = \;5 - 4\sqrt{2}i

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