To simplify (-10-i)/(-9-6i), multiply both sides by the denominator's conjugate (-9+6i). Expand, combine real and imaginary parts, and divide each term. The final answer in a+bi form is: 1.1111 - 0.6667i.
To simplify the expression (-10-i)/(-9-6i) into a+bi form, we can follow these steps:
Rationalize the denominator: Multiply both numerator and denominator by the complex conjugate of the denominator, which is -9+6i. This will eliminate the imaginary unit in the denominator, making it easier to work with.
(-10-i)/(-9-6i) = [(−10−i) * (-9+6i)] / [(-9-6i) * (-9+6i)]
Expand the products:**
[-10*(-9) + (-10)(6)i + (-1)i(-9) + (-1)i*(6)i^2] / [-9*(-9) - 9*(6)i + (-6)i*(-9) + (-6)i*(6)i^2]
Simplify the terms:
[90 - 60i + 9i + 6i^2] / [81 + 54i + 54i + 36]
Combine real and imaginary parts:
(90 + 6) / (81 + 36) + (9 - 60)i / (81 + 36)
Divide each term separately:
1.1111 - 0.6667i
Therefore, the complex number in simplest a+bi form is 1.1111 - 0.6667i.