Question

Find the real numbers x and y that make the equation true:
-4+yi=x+3i

Answer 1

The real terms must be equal and the imaginary terms must be equal.
x = -4
yi = 3i
y = 3
So we have:
x = -4 and y = 3

Answer 2

for any equation
a+bi=c+di
the real and imaginary parts must be equal
in other words, a=c and b=d

-4+yi=x+3i
therefor
-4=x
yi=3i
y=3

x=-4
y=3
(-4,3)