How do you simplify (3i)/(9-6i)3i9−6i?

1 Answer
mason m
Dec 31, 2015

-2/13+3/13i−213+313i

Explanation:

Divide each term by 33.

=>i/(3-2i)⇒i3−2i

Now, to remove the imaginary part from the denominator and write the answer as a complex number in the form a+bia+bi, multiply the fraction by the complex conjugate of the denominator.

=>i/(3-2i)((3+2i)/(3+2i))⇒i3−2i(3+2i3+2i)

Distribute. Notice that the bottom will form a difference of squares.

=>(3i+2i^2)/(9-4i^2)⇒3i+2i29−4i2

To continue simplifying, rewrite i^2i2 as -1−1. i^2=-1i2=−1 since i=sqrt(-1)i=√−1.

=>(3i+2(-1))/(9-4(-1))=(-2+3i)/13⇒3i+2(−1)9−4(−1)=−2+3i13

Split apart the numerator to write in a+bia+bi form.

=>-2/13+3/13i⇒−213+313i

Related questions
See all questions in Complex Number Plane
Impact of this question
2867 views around the world
You can reuse this answer
Creative Commons License