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

1 Answer
Jan 8, 2017

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