Questions: Divide. (6-6 i)/(5+6 i)

To divide two complex numbers, multiply the numerator and the denominator by the conjugate of the denominator. This will eliminate the imaginary part in the denominator, allowing you to simplify the expression.

We start with the complex numbers: \[ \text{Numerator} = 6 - 6i \] \[ \text{Denominator} = 5 + 6i \]

The conjugate of the denominator \(5 + 6i\) is: \[ \text{Conjugate Denominator} = 5 - 6i \]

We multiply both the numerator and the denominator by the conjugate of the denominator: \[ \frac{(6 - 6i)(5 - 6i)}{(5 + 6i)(5 - 6i)} \]

Calculating the denominator: \[ (5 + 6i)(5 - 6i) = 5^2 - (6i)^2 = 25 + 36 = 61 \]

Calculating the numerator: \[ (6 - 6i)(5 - 6i) = 30 - 36i - 30i + 36i^2 = 30 - 66i - 36 = -6 - 66i \]

Thus, we have: \[ \frac{-6 - 66i}{61} \]

This simplifies to: \[ -\frac{6}{61} - \frac{66}{61}i \]

The final result is: \[ \boxed{-0.0984 - 1.08197i} \]