Question

How do you divide `(-6-i)/(1+5i)`?

Answer 1

I multiply by 1 in form of the complex conjugate of the denominator divided by itself, use the F.O.I.L. method to multiply the numerator, and then simplify.

Explanation:

Given: `(-6 - i)/(1 + 5i)`

Multiply by 1 in the form of `(1 - 5i)/(1 - 5i)`:

`(-6 - i)/(1 + 5i)(1 - 5i)/(1 - 5i)`

The denominator becomes the difference of two squares:

`((-6 - i)(1 - 5i))/(1^2 - (5i)^2)`

`((-6 - i)(1 - 5i))/(1 - 25i^2)`

Use the F.O.I.L method to multiply the numerator:

`(-6 + 30i - i + 5i^2)/(1 - 25i^2)`

Substitute -1 for `i^2`

`(-6 + 30i - i - 5)/(1 + 25)`

Combine like terms:

`(-11 + 29i)/26`

Divide each term:

`-11/26 + 29/26i`