Hi there I need help with rationalize the denominator

Question

Rationalize the denominator

1. 1/-8-5i
2. 1/-2-8i
3. 4/-3-6i
4. -10-5i/-6+6i

Answer 1

To rationalize the denominator means to multiply the original fraction by a fraction, valued at 1, that has the conjugate of the denominator (for a - bi, use a + bi) in the numerator and denominator to eliminate the imaginary term (i) from the denominator.

1 X -8 + 5i = -8 + 5i = -8 + 5i = -8 + 5i

-8 - 5i -8 + 5i 64 - 25i^2 64 + 25 89

Answer 2

If the fraction is 1/(a+bi), multiply by (a-bi)/(a-bi) to rationalize it.