00:01
In your question, you're asked to find the quotient of these complex numbers.
00:04
So what we first want to do is write this in a fraction format for division.
00:11
Now to divide by complex numbers, we actually multiply both the numerator and the denominator by what is called the conjugate of the denominator.
00:21
So the conjugate is the same expression, just with a different or opposite middle sign.
00:28
So we're going to multiply by 2 plus 5i for top and bottom.
00:37
Now, for the numerator, we have to go through and use the distributive property.
00:42
Four is going to multiply both of these values, so that's going to give me an 8 plus 20i.
00:48
Then the negative 6i has to multiply both values.
00:52
That's going to give me a minus 12i minus 30i squared.
01:01
Now in the denominator, we do the same thing.
01:05
We have to multiply them, so i'm going to take the 2 times 2 and the 2 times 5i, so so that's 4 plus 10i.
01:12
Then we would have the negative 5i multiply both of these...