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5 April, 05:42

You know 4-3i is the complex conjugate of 4+3i. If you multiply the denominator of - 2+5i4+3i by 4-3i, what will you get? Enter your answer as a number, like this: 42 Algebra 2

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  1. 5 April, 05:45
    0
    25

    Step-by-step explanation:

    Given

    (-2 + 5i) / (4 + 3i)

    Required

    Multiply the denominator by 4 - 3i

    The denominator of the fraction above is 4 + 3i

    When multiplied by 4 - 3i, the result is as follows;.

    Result = (4 + 3i) (4 - 3i)

    Expand

    Result = 4 (4 - 3i) + 3i (4 - 3i)

    Open both brackets (take it one at a time)

    Result = 4 * 4 - 4 * 3i + 3i (4 - 3i)

    Result = 16 - 12i + 3i (4 - 3i)

    Open the second bracket

    Result = 16 - 12i + 12i - 3i * 3i

    Result = 16 - 12i + 12i - 9i²

    In complex numbers, i = √-1

    i² = (√-1) ²

    i² = √-1 * √-1

    i² = - 1

    The expression

    Result = 16 - 12i + 12i - 9i²

    Becomes

    Result = 16 - 12i + 12i - 9 (-1)

    Result = 16 - 12i + 12i + 9

    Collect like terms

    Result = 16 + 9 + 12i - 12i

    Result = 25 + 0

    Result = 25

    Hence, when the denominator of the fraction is multiplied by 4 - 3i, the result is 25
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