Question

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

Accepted Answer

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

Answer

x(1+2i)+y(2-i)=4+3i
To find x and y:
x(1+2i)+y(2-i)=4+3i
We open the brackets :
x+2xi +2y-yi = 4+3i
We collect the  reals of the left together. And similarly collect the imaginary numbers  of the left together.
(x+2y) +(2x-y)i = 4+3i
We equate real parts on both sides: x+2y = 4......(1)
We equate the imaginary parts on both sides: 2x-y = 3....(2)
(1)+2*(2): x +2*2x= 4+2*3 = 10. So 5x = 10. So x= 10/5 = 2.
Put x = 2 in (2) : 2*2-y = 3. Or -y = 3-4 = -1. So y = 1.
Therefore x= 2 and y = 1.

Answer

To determine x and y, we'll have to re-write the left side as a complex number put in rectangular form:
z = a + b*i
We'll have to identify the real part a and the imaginary part b.
We'll start by removing the brackets:
x + 2ix + 2y - iy = 4 + 3i
We'll combine the real parts and the imaginary parts from the left side:
(x+2y) + i(2x - y) = 4 + 3i
We'll compare both sides and we'll get:
x + 2y = 4 (1)
2x - y = 3 (2)
We'll add (1) + 2*(2):
x + 2y + 4x - 2y = 4 + 6
We'll combine and eliminate like terms:
5x = 10
We'll divide by 5:
x = 2
We'll substitute x in (1):
2 + 2y = 4
2y = 2
y = 1
The valid values for x and y are: x = 2 and y = 1.

Math

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

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