Question

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

Answer 1

x=4 y=-5

Step-by-step explanation:

took the test and got a 100

Answer 2

Answer: The value of x and y are all points which satisfies the equation
`4y+5x=0`, i.e.,(4,-5).

Step-by-step explanation:

The given expression is,

`(4+5i)(x+yi)`

Use distributive property to simplify the expression.

`4(x+yi)+5i(x+yi)`

`4x+4yi+5ix+5yi^2`

We know that
`i^2=-1`

`4x+4yi+5ix-5y`

Combine likely terms,

`(4x-5y)+i(4y+5x)`

In x+iy, x is the real part is iy is imaginary part. If the given expression represents a real number it means the imaginary part must be 0.

`4y+5x=0`

All the points which satisfies the above equation are the values of x and y for which the given expression is a real number.

Fom eg. (4,-5)

`4(-5)+5(4)=0`

`0=0`

LHS=RHS, it means the point satisfies the equation and the value of x and y are (4,-5).