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Algebra

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Will you explain the concept of "i" in algebra?

Problem: 4+2i/4-2i

  • Algebra -

    i = sqrt (-1)
    so i^2 = sqrt (-1)(sqrt(-1) = -1

    (4+2i)/(4-2i)

    to get rid of i in the denominator multiply top and bottom by the "comlex conjugate of (4-2i) which is (4+2i)

    Rule: conjugate of (a-bi) is (a+bi)

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

    16 + 16 i +4 i^2
    =-------------------
    (16 - 2 i^2)

    but we all know that i^2 = -1 so

    12 + 16 i
    ----------
    18

    or

    6 + 8 i
    --------
    9

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