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

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

anonymous · Answer

x = 4, y = –5

==========reasoning =========

To make it real you want no i's in the resulting equation which means no middle term.

x = 4, y = –5 is the only pair that gets rid of the middle term.  The last terms cancel automatically because i^2 = -1