How do you divide #(3 + 2i) / (2 - 6i)#?

1 Answer
Mar 28, 2016

Answer:

You must multiply the whole expression by the conjugate of the denominator, just like you did when you were younger when you were to rationalize the denominator.

Explanation:

The conjugate forms a difference of squares. Therefore, to find it, you must switch the sign in the middle.

Thus, the conjugate is #2 + 6i#

#(3 + 2i)/(2 - 6i) xx (2 + 6i)/(2 + 6i)#

Now multiply. Don't forget that #i^2 = -1#

#(6 + 4i + 12i - 12)/(4 - (36 xx -1)#

Don't forget that you can combine #i#'s with #i#'s but you cannot combine non #i's# with #i's#.

#(6 + 16i - 12)/40#

#(-6 + 16i)/40#

This is as simplified as possible.

Practice exercises:

  1. Evaluate:

a). #(4 + 2i)/(3 - 5i)#

b). #(4x + 3i)/(-x + 2i)#

Good luck!