00:01
We're being asked to simplify the given expression.
00:03
Remember, you can't be left with a complex number in your denominator of the fraction.
00:07
So to get rid of it, we're going to need to multiply both the numerator and the denominator by its conjugate.
00:12
Well, the conjugate of 5 minus 12i is 5 plus 12i.
00:16
So we're going to multiply the numerator and denominator by 5 plus 12i.
00:22
So in the numerator, we just need to distribute.
00:25
Well, 13 times 5 is 65, and 13 times 12i is positive 15.
00:33
Now, for our denominator, when we multiply conjugates, all you need to do is multiply the first and last terms, because remember, the middle terms will cancel.
00:42
Well, 5 times 5 is 25, and negative 12i times positive 12i is negative 144 i squared.
00:52
Well, we can't simplify the numerator, so we can just simply bring that down.
00:56
So we'll have 65 plus 156i.
01:00
And in denominator, we have i squared...