Answer:
x = 4 and y = - 5
Step-by-step explanation:
note that the product of a complex number and it's conjugate is real
That is
(a + bi)(a - bi) where a, b are real
= a² - abi + abi - b²i²
= a² + b² ← a real number
For (4 + 5i)(x + yi) to be real
we require (x + yi) to be the conjugate of 4 + 5i , that is 4 - 5i
(4 + 5i)(4 - 5i) ⇒ x = 4 and y = - 5
Answer:

Step-by-step explanation:
Given

Required
The equivalent expression
We have:

Expand

Further expand

Apply laws of indices

Most of the time for coordinate planes, they are asking you to plot the point correctly, and to state which quadrant the point falls into.
The Quadrant points start at (+ , +) for Quadrant I, and moves clockwise. See attached picture.
Quadrant I: (+ , +)
Quadrant II: (+ , -)
Quadrant III: (- , -)
Quadrant IV: (- , +)
Remember, the point is split into two parts, in which the first one is x (which signifies the placement for the horizontal line), while the other is y (which signifies the placement for the vertical line).
~
Just by giving the numbers an analisys, we are able to find the answer, specially because we have options to choose from.
32 is a big part of 48. It's more than half, which would be 24 and would correspond to 50%. Therefore, nor 46 nor 33 can be answers, because 32 is more than the half of 48, so the answer is A.
Hope it helped,
BioTeacher101