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

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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

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