How do I simplify this?

(4+2i)/(-4-6i)

2 Answers
May 16, 2018

(-1 + 4i) / 13

Explanation:

Multiply the Numerator and Denominator by the Conjugate of the Denominator.
The Conjugate is exactly like the Denominator except the sign on the imaginary number is different.
(4+2i)/(-4-6i) * (-4+6i)/(-4 + 6i)

Multiply by Distribution on Numerator and Denominator.
= (-16 + 24i - 8i - 12i^2)/(16 - 24i + 24i - 36i^2)

Note: i = sqrt(-1) so i^2 = -1
Combine Like Terms and Replace i^2 with -1
= (-16 + 16i - 12(-1)) / (16 - 36(-1))
= (-16 + 16i + 12) / (16 + 36)
= (-4 + 16i) / 52

Simplify by Dividing all Numbers by 4:
= (-1 + 4i) / 13

May 16, 2018

Given

(4+2i)/(-4-6i)

From inspection we see that both in the numerator and denominator factor 2 can be taken out as common. This cancels out. Therefore, we get

-(2(2+i))/(2(2+3i))
=>-((2+i))/((2+3i))

Multiplying and dividing with complex conjugate of denominator we get

-((2+i))/((2+3i))xx(2-3i)/(2-3i)
=>-((2+i)(2-3i))/((2)^2-(3i)^2)
=>-(4-6i+2i-3i^2)/((2)^2-(3i)^2)
=>-(7-4i)/(13)
=>(4i-7)/(13)