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.