(1+2i)*x+(3-5i)*y=1-3i

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Solution for (1+2i)*x+(3-5i)*y=1-3i equation: 


Simplifying
(1 + 2i) * x + (3 + -5i) * y = 1 + -3i

Reorder the terms for easier multiplication:
x(1 + 2i) + (3 + -5i) * y = 1 + -3i
(1 * x + 2i * x) + (3 + -5i) * y = 1 + -3i

Reorder the terms:
(2ix + 1x) + (3 + -5i) * y = 1 + -3i
(2ix + 1x) + (3 + -5i) * y = 1 + -3i

Reorder the terms for easier multiplication:
2ix + 1x + y(3 + -5i) = 1 + -3i
2ix + 1x + (3 * y + -5i * y) = 1 + -3i

Reorder the terms:
2ix + 1x + (-5iy + 3y) = 1 + -3i
2ix + 1x + (-5iy + 3y) = 1 + -3i

Reorder the terms:
2ix + -5iy + 1x + 3y = 1 + -3i

Solving
2ix + -5iy + 1x + 3y = 1 + -3i

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '3i' to each side of the equation.
2ix + -5iy + 1x + 3i + 3y = 1 + -3i + 3i

Reorder the terms:
3i + 2ix + -5iy + 1x + 3y = 1 + -3i + 3i

Combine like terms: -3i + 3i = 0
3i + 2ix + -5iy + 1x + 3y = 1 + 0
3i + 2ix + -5iy + 1x + 3y = 1

Add '-1x' to each side of the equation.
3i + 2ix + -5iy + 1x + -1x + 3y = 1 + -1x

Combine like terms: 1x + -1x = 0
3i + 2ix + -5iy + 0 + 3y = 1 + -1x
3i + 2ix + -5iy + 3y = 1 + -1x

Add '-3y' to each side of the equation.
3i + 2ix + -5iy + 3y + -3y = 1 + -1x + -3y

Combine like terms: 3y + -3y = 0
3i + 2ix + -5iy + 0 = 1 + -1x + -3y
3i + 2ix + -5iy = 1 + -1x + -3y

Reorder the terms:
-1 + 3i + 2ix + -5iy + x + 3y = 1 + -1x + -3y + -1 + x + 3y

Reorder the terms:
-1 + 3i + 2ix + -5iy + x + 3y = 1 + -1 + -1x + x + -3y + 3y

Combine like terms: 1 + -1 = 0
-1 + 3i + 2ix + -5iy + x + 3y = 0 + -1x + x + -3y + 3y
-1 + 3i + 2ix + -5iy + x + 3y = -1x + x + -3y + 3y

Combine like terms: -1x + x = 0
-1 + 3i + 2ix + -5iy + x + 3y = 0 + -3y + 3y
-1 + 3i + 2ix + -5iy + x + 3y = -3y + 3y

Combine like terms: -3y + 3y = 0
-1 + 3i + 2ix + -5iy + x + 3y = 0

The solution to this equation could not be determined.

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