(x+4y)+(2x-3y)i=13+7i

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Solution for (x+4y)+(2x-3y)i=13+7i equation: 


Simplifying
(x + 4y) + (2x + -3y) * i = 13 + 7i

Remove parenthesis around (x + 4y)
x + 4y + (2x + -3y) * i = 13 + 7i

Reorder the terms for easier multiplication:
x + 4y + i(2x + -3y) = 13 + 7i
x + 4y + (2x * i + -3y * i) = 13 + 7i
x + 4y + (2ix + -3iy) = 13 + 7i

Reorder the terms:
2ix + -3iy + x + 4y = 13 + 7i

Solving
2ix + -3iy + x + 4y = 13 + 7i

Solving for variable 'i'.

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

Add '-7i' to each side of the equation.
2ix + -3iy + x + -7i + 4y = 13 + 7i + -7i

Reorder the terms:
-7i + 2ix + -3iy + x + 4y = 13 + 7i + -7i

Combine like terms: 7i + -7i = 0
-7i + 2ix + -3iy + x + 4y = 13 + 0
-7i + 2ix + -3iy + x + 4y = 13

Add '-1x' to each side of the equation.
-7i + 2ix + -3iy + x + -1x + 4y = 13 + -1x

Combine like terms: x + -1x = 0
-7i + 2ix + -3iy + 0 + 4y = 13 + -1x
-7i + 2ix + -3iy + 4y = 13 + -1x

Add '-4y' to each side of the equation.
-7i + 2ix + -3iy + 4y + -4y = 13 + -1x + -4y

Combine like terms: 4y + -4y = 0
-7i + 2ix + -3iy + 0 = 13 + -1x + -4y
-7i + 2ix + -3iy = 13 + -1x + -4y

Reorder the terms:
-13 + -7i + 2ix + -3iy + x + 4y = 13 + -1x + -4y + -13 + x + 4y

Reorder the terms:
-13 + -7i + 2ix + -3iy + x + 4y = 13 + -13 + -1x + x + -4y + 4y

Combine like terms: 13 + -13 = 0
-13 + -7i + 2ix + -3iy + x + 4y = 0 + -1x + x + -4y + 4y
-13 + -7i + 2ix + -3iy + x + 4y = -1x + x + -4y + 4y

Combine like terms: -1x + x = 0
-13 + -7i + 2ix + -3iy + x + 4y = 0 + -4y + 4y
-13 + -7i + 2ix + -3iy + x + 4y = -4y + 4y

Combine like terms: -4y + 4y = 0
-13 + -7i + 2ix + -3iy + x + 4y = 0

The solution to this equation could not be determined.

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