I think the exactly answer indigenous the choices detailed above is alternative C. The worths of x and y that would certainly make the expression to represent a genuine number would be that x = 4, y = –5. Substituting and also simplifying,(4 + 5i)(4 - 5i)16 - 20i + 20i - 25i²16 - 25(-1)16 +2541

x = 4, y = -5

Further explanation

This is a problem with complicated numbers.

A complicated number is a variety of the form where x and also y room both actual numbers.

x is thought about the real component of the complex number. Y is taken into consideration the imaginary part of the complicated number.The real part of a facility number is denoted through
The imaginary component of a complicated number is denoted by
The modulus of a complicated number
is denoted through
and defined to it is in
Remember this

For example,

Re(z) = 3Im(z) = -4The modulus

Let"s look at the vital problem.

You are watching: Which values of x and y would make the following expression represent a real number?

We must identify the values of x and also y that would make the complying with expression represent a genuine number.

At this point, 4yi and also 5xi should be of equal value and significant opposite, so the the expression represents genuine numbers.

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Become a fraction, i.e.,

From the options, the price is C.

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Let"s check ago to expression.

x = 4 dan y = - 5 ⇒

Thus the expression represent a real number of 41.