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Math Help - Imaginary Numbers

  1. #1
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    Imaginary Numbers

    Having trouble with the following problem:

    (2 + 2i) (3 - 4i)

    I have worked out this much so far.

    6 - 8i + 6i - 8i^2

    6 - 2i - 8i^2

    Since there is an "i" squared, do i distribute that with the preceding "8" coefficient?

    Also running into a problem solving the following word problem:

    "The sum of the squares of two consecutive positive odd integers is 514. What are the integers?"

    I have it set up as x^2 + (x+2)^2 = 514

    x^2 + x^2 + 4x + 4 = 514

    2x^2 + 4x = 510

    Thanks again for everyone's help!
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  2. #2
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    Quote Originally Posted by Hapa View Post
    Since there is an "i" squared, do i distribute that with the preceding "8" coefficient?
    By definition, i^2=-1. Substitute this into your expression.

    "The sum of the squares of two consecutive positive odd integers is 514. What are the integers?"

    I have it set up as x^2 + (x+2)^2 = 514

    x^2 + x^2 + 4x + 4 = 514

    2x^2 + 4x = 510
    You should be able to factor this:

    2x^2+4x-510=0

    \Rightarrow x^2+2x-255=0

    Can you break -255 into two factors whose sum is 2? Start by listing the possible factorizations of -255:

    -255\cdot1\qquad255\cdot-1

    -17\cdot15\qquad17\cdot-15

    -5\cdot51\qquad5\cdot-51

    -3\cdot85\qquad3\cdot-85

    Now which pair adds up to +2?
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