Which values of x and y would make the following expression represent a real number? (4+5i)(x+ yi) Ox=4,y= 5
Ox=-4, y = 0
Ox=4, y=-5
Ox=0, y= 5

C

Step-by-step explanation:

We have the expression and we want to find the values of and such that the expression will evaluate to a real number.

So, let's first expand the expression. Distribute:

Distribute:

Simplify:

So, we want to make the second part within the real numbers.

Notice that we only have two ways of doing this: 1) Either both and are imaginary numbers themselves canceling out the , or 2), the entire expression equals 0.

Since our answer choices consists of only real numbers, this means that the imaginary part must be equal to 0. So:

We can divide everything by :

Now, we can use our answer choices.

Running down the list, we can see that the choice that works is C. If we substitute the values of C into the equation, we get:

Therefore, our answer is C.