00:01
For this problem, we're told the x is equal to 4i, and we need to use that to simplify 1 plus 2x divided by x plus 3.
00:11
So if we plug in x is equal to 4i, we get 1 plus 8i divided by 4i plus 3.
00:32
And now, when we have complex numbers, we don't want to keep an i in the denials.
00:42
So to get rid of the i in the denominator, what we usually do is we multiply by the what's called the conjugate, which is equal to negative 4i plus 3.
01:01
And so all you do is you write the same thing as you had in the denominator, but add a negative sign to the part with the i.
01:17
And so the reason that you can do this is because if you take any number and you divide it by itself, it's just equal to one.
01:35
So the part we have in green here is just equal to one.
01:38
And you can multiply anything by one because it stays equal.
01:42
So now if we multiply things out, in the denominator, we have a 4i times negative 4i.
01:52
So that is equal to negative 16 i squared.
01:57
The i squared is negative 1, so we just get a positive 16.
02:03
And then we have plus 3 times negative 4i, but then we also have plus 3 times positive 4i...