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

##### 1 Answer

Dec 31, 2015

#### Explanation:

Divide each term by

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

Now, to remove the imaginary part from the denominator and write the answer as a complex number in the form **complex conjugate** of the denominator.

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

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

#=>(3i+2i^2)/(9-4i^2)#

To continue simplifying, rewrite

#=>(3i+2(-1))/(9-4(-1))=(-2+3i)/13#

Split apart the numerator to write in

#=>-2/13+3/13i#