Question

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

Answer 1

The product will be a real number when x = 4 and y = -5.

Which values of x and y should we use?

We have the product of complex numbers:

$(4 + 5i)*(x + yi)$

We want this to be a real number, then the second complex number must be the complex conjugate of the first one, so we must have:

$(x + yi) = (4 - 5i)$

Now, if we take the product, we get:

$(4 + 5i)*(4 - 5i)\\\\4*4 - 4*5i + 4*5i - (5*5)*i^2 = 16 + 25 = 41$

So we can see that the outcome is a real number.

Then we must have x = 4 and y = -5.

If you want to learn more about complex numbers:

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