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.

See more: In Which Type Of Chemical Bonding Are Electrons Shared Between Adjacent Atoms

*

Become a fraction, i.e.,

*

From the options, the price is C.

*

- - - - - - -

Let"s check ago to expression.

x = 4 dan y = - 5 ⇒

*

*

Thus the expression represent a real number of 41.

Learn moreThe midpoint The piecewise-defined functions The composite role

Keywords: identify, the worths of x and also y, the complying with expression, represent a real number, (4 + 5i)(x + yi), a facility number, real, imaginary