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How to simplify this: 7-29i over 8-13i?

4 Answers

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  • 4 years ago
    Favorite Answer

    (7 - 29i) / (8 - 13i)

    You have the division of two complex numbers. You want to rationalize the denominator by multiplying both halves of this fraction by the denominator's conjugate. Which in this case is (8 + 13i).

    So we get:

    (7 - 29i)(8 + 13i) / [(8 + 13i)(8 - 13i)]

    Now FOIL both halves of the fraction. If you do everything right, the denominator should be a rational value at the end:

    (56 + 91i - 232i - 377i²) / (64 - 104i + 104i - 169i²)

    (56 - 141i - 377i²) / (64 - 169i²)

    Recall that i² = -1, so:

    (56 - 141i + 377) / (64 + 169)

    (433 - 141i) / 233

    So putting this back into complex form:

    (433/233) - (141/233)i

  • ?
    Lv 7
    4 years ago

    1/(a+bi) = (a-bi)/(a²+b²)

    multiply top and bottom by the conjugate of the denominator.

  • 4 years ago

    Dividing by 8 - 13i is the same as multiplying by (8 + 13i)/(8^2 + 13^2) = (8 + 13i)/233.

    So just work out (7 - 29i)(8 + 13i)/233.

  • alex
    Lv 7
    4 years ago

    (7-29i) over (8-13i) = [(7-29i)( 8+13i)/[(8-13i) (8+13i) ] = ...expand and simplify

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