(4x+3y)+(2x-y)i=18-6i

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Solution for (4x+3y)+(2x-y)i=18-6i equation:


Simplifying
(4x + 3y) + (2x + -1y) * i = 18 + -6i

Remove parenthesis around (4x + 3y)
4x + 3y + (2x + -1y) * i = 18 + -6i

Reorder the terms for easier multiplication:
4x + 3y + i(2x + -1y) = 18 + -6i
4x + 3y + (2x * i + -1y * i) = 18 + -6i
4x + 3y + (2ix + -1iy) = 18 + -6i

Reorder the terms:
2ix + -1iy + 4x + 3y = 18 + -6i

Solving
2ix + -1iy + 4x + 3y = 18 + -6i

Solving for variable 'i'.

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

Add '6i' to each side of the equation.
2ix + -1iy + 4x + 6i + 3y = 18 + -6i + 6i

Reorder the terms:
6i + 2ix + -1iy + 4x + 3y = 18 + -6i + 6i

Combine like terms: -6i + 6i = 0
6i + 2ix + -1iy + 4x + 3y = 18 + 0
6i + 2ix + -1iy + 4x + 3y = 18

Add '-4x' to each side of the equation.
6i + 2ix + -1iy + 4x + -4x + 3y = 18 + -4x

Combine like terms: 4x + -4x = 0
6i + 2ix + -1iy + 0 + 3y = 18 + -4x
6i + 2ix + -1iy + 3y = 18 + -4x

Add '-3y' to each side of the equation.
6i + 2ix + -1iy + 3y + -3y = 18 + -4x + -3y

Combine like terms: 3y + -3y = 0
6i + 2ix + -1iy + 0 = 18 + -4x + -3y
6i + 2ix + -1iy = 18 + -4x + -3y

Reorder the terms:
-18 + 6i + 2ix + -1iy + 4x + 3y = 18 + -4x + -3y + -18 + 4x + 3y

Reorder the terms:
-18 + 6i + 2ix + -1iy + 4x + 3y = 18 + -18 + -4x + 4x + -3y + 3y

Combine like terms: 18 + -18 = 0
-18 + 6i + 2ix + -1iy + 4x + 3y = 0 + -4x + 4x + -3y + 3y
-18 + 6i + 2ix + -1iy + 4x + 3y = -4x + 4x + -3y + 3y

Combine like terms: -4x + 4x = 0
-18 + 6i + 2ix + -1iy + 4x + 3y = 0 + -3y + 3y
-18 + 6i + 2ix + -1iy + 4x + 3y = -3y + 3y

Combine like terms: -3y + 3y = 0
-18 + 6i + 2ix + -1iy + 4x + 3y = 0

The solution to this equation could not be determined.

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