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Thread: Squares, complete the square, complex numbers, quadratic formula, discriminant

  1. #1
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    Squares, complete the square, complex numbers, quadratic formula, discriminant

    Test next week, need some help with my assignments.

    First completing the square: $\displaystyle x^2-8x+32=0$
    I've done it 4 different ways and I've deduced that it is either
    $\displaystyle -4+8i, -4-8i$
    $\displaystyle -4+4i, -4-4i$
    $\displaystyle 4+8i, 4-8i$
    $\displaystyle 4+4i, 4-4i$

    Okay.. Second.. This needs to be written in standard form.
    $\displaystyle \frac{8-7i}{3-4i}$

    Third, and last for the moment. Solve the equation:
    $\displaystyle -x^2+4=2x^2-5$

    More to come once I get to them.
    Last edited by jscalalamoboy; Dec 21st 2009 at 06:18 PM.
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  2. #2
    Super Member Quacky's Avatar
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    Idk number 2, but here're my attempts at one and 3:

    1)

    $\displaystyle (x-4)^2-4^2+32=0$
    $\displaystyle
    (x-4)^2=-16
    $
    $\displaystyle (x-4)= \sqrt{-16} = 4i$
    $\displaystyle
    x= 4+4i, x=4-4i
    $

    3)
    $\displaystyle -x^2+4=2x^2-5$
    $\displaystyle 4=3x^2-5$
    $\displaystyle 9=3x^2$
    $\displaystyle 3=x^2$
    $\displaystyle x=\sqrt{3}$
    Last edited by Quacky; Feb 5th 2010 at 05:29 PM.
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  3. #3
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    2)
    standar form is x+iy.

    try multiplying the numerator and denominator of that expression by the conjugate of the denominator. the conjugate of a+ib is a-ib.
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