Solve for x and y 12ix 12iy 1 iSolutionWell note the com

Solve for x and y : (1-2i)*x + (1+2i)*y = 1 + i

Solution

We\'ll note the complex number from the left side as z1 and the complex number from the right side as z2.

For z1 = z2, we\'ll have to impose the following conditions:

Re(z1) = Re(z2)

Im(z1) = Im(z2)

To determine the real and imaginar parts of the complex number from the left side, we\'ll have to remove the brackets:

(1-2i)*x + (1+2i)*y = x - 2ix + y + 2iy

We\'ll combine the real parts and imaginary parts:

Re(z1) = x+y

Im(z1) = -2x + 2y

Re(z2) = 1

Im(z2) = 1

x+y = 1 (1)

-2x + 2y = 1 (2)

We\'ll multiply by 2 (1):

2x + 2y = 2 (3)

We\'ll add (3) to (2):

2x + 2y - 2x + 2y = 2+1

We\'ll eliminate like terms:

4y = 3

y = 3/4

We\'ll substitute y in (1):

x+y = 1

x + 3/4 = 1

x = 1 - 3/4

x = (4-3)/4

x = 1/4