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Math Help - Complex

  1. #1
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    Complex

    (a) Show that (3 i)^2 = 8 6i.

    (b) The quadratic equation
    az^2 + bz + 10i = 0,
    where a and b are real, has a root 3 i.
    (i) Show that a = 3 and find the value of b.
    (ii) Determine the other root of the equation, giving your answer in the form p + iq.
    (Hint for (ii): Use the fact that the sum of the roots in any quadratic is b/a).
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  2. #2
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    a) (3-i)^2=3^2-2(3)(i)+i^2=9-6i-1=8-6i.

    b)
    i) a(3-i)^2+b(3-i)+10i=0 then 8a+3b=0 , 10-6a-b=0 hence a=3 , b=-8

    ii) \frac{-b}{a}=(3-i)+(p+qi)=\frac{-(-8)}{3} then p=\frac{-1}{3} , q=1 hence, other root is \frac{-1}{3}+i.
    Last edited by bigli; June 7th 2010 at 06:12 AM.
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