What are x and y? x(1+2i)+y(2-i)=4+3i

x(1+ 2i) + y( 2-i) = 4 +
3i

Let us expand the
brackets.

==> x + 2xi + 2y - yi = 4 +
3i.

==> We will combine real terms and complex terms
together.

==> (x+ 2y) + (2x -y) i = 4 +
3i.

Now we will compare
terms.

==> x + 2y = 4
..............(1)

==> 2x - y = 3
....................(2)

Now we will solve the
system.

We will use the substitution method to
solve.

==> We will rewrite y= 2x -
3.

==> x+ 2y =
4

==> x + 2(2x-3) =
4

==> x + 4x - 6 =
4

==> 5x =
10

==> x=
2.

==> y= 2x -3 = 2*2 - 3 = 4-3
=1

==> y=
1