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Divide the complex numbers and express your answer in the form (a + bi). 5 - 4i /8 + 6i

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Final answer:

To divide complex numbers and express the answer in the form (a + bi), we can use the concept of complex conjugates. The division of the complex numbers 5 - 4i and 8 + 6i is (16 - 62i) / 100.

Step-by-step explanation:

To divide complex numbers and express the answer in the form (a + bi), we can use the concept of complex conjugates. The complex conjugate of a complex number in the form a + bi is a - bi. In this case, the complex conjugate of 8 + 6i is 8 - 6i.

Using the division formula for complex numbers, we have:

(5 - 4i) / (8 + 6i) = [(5 - 4i) * (8 - 6i)] / [(8 + 6i) * (8 - 6i)]

Expanding and simplifying the numerator and denominator, we get:

(40 - 30i - 32i + 24i^2) / (64 - 36i^2)

Combining like terms and simplifying further, we obtain:

(16 - 62i) / 100

So, the division of the complex numbers 5 - 4i and 8 + 6i is (16 - 62i) / 100.

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