2x+1+(3+y)i=x-3+(12-2y)i

Solution for 2x+1+(3+y)i=x-3+(12-2y)i equation:

Simplifying
2x + 1 + (3 + y) * i = x + -3 + (12 + -2y) * i

Reorder the terms for easier multiplication:
2x + 1 + i(3 + y) = x + -3 + (12 + -2y) * i
2x + 1 + (3 * i + y * i) = x + -3 + (12 + -2y) * i
2x + 1 + (3i + iy) = x + -3 + (12 + -2y) * i

Reorder the terms:
1 + 3i + iy + 2x = x + -3 + (12 + -2y) * i

Reorder the terms for easier multiplication:
1 + 3i + iy + 2x = x + -3 + i(12 + -2y)
1 + 3i + iy + 2x = x + -3 + (12 * i + -2y * i)
1 + 3i + iy + 2x = x + -3 + (12i + -2iy)

Reorder the terms:
1 + 3i + iy + 2x = -3 + 12i + -2iy + x

Solving
1 + 3i + iy + 2x = -3 + 12i + -2iy + x

Solving for variable 'i'.

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

Add '-12i' to each side of the equation.
1 + 3i + iy + -12i + 2x = -3 + 12i + -2iy + -12i + x

Reorder the terms:
1 + 3i + -12i + iy + 2x = -3 + 12i + -2iy + -12i + x

Combine like terms: 3i + -12i = -9i
1 + -9i + iy + 2x = -3 + 12i + -2iy + -12i + x

Reorder the terms:
1 + -9i + iy + 2x = -3 + 12i + -12i + -2iy + x

Combine like terms: 12i + -12i = 0
1 + -9i + iy + 2x = -3 + 0 + -2iy + x
1 + -9i + iy + 2x = -3 + -2iy + x

Add '2iy' to each side of the equation.
1 + -9i + iy + 2iy + 2x = -3 + -2iy + 2iy + x

Combine like terms: iy + 2iy = 3iy
1 + -9i + 3iy + 2x = -3 + -2iy + 2iy + x

Combine like terms: -2iy + 2iy = 0
1 + -9i + 3iy + 2x = -3 + 0 + x
1 + -9i + 3iy + 2x = -3 + x

Add '-1' to each side of the equation.
1 + -9i + 3iy + -1 + 2x = -3 + -1 + x

Reorder the terms:
1 + -1 + -9i + 3iy + 2x = -3 + -1 + x

Combine like terms: 1 + -1 = 0
0 + -9i + 3iy + 2x = -3 + -1 + x
-9i + 3iy + 2x = -3 + -1 + x

Combine like terms: -3 + -1 = -4
-9i + 3iy + 2x = -4 + x

Add '-2x' to each side of the equation.
-9i + 3iy + 2x + -2x = -4 + x + -2x

Combine like terms: 2x + -2x = 0
-9i + 3iy + 0 = -4 + x + -2x
-9i + 3iy = -4 + x + -2x

Combine like terms: x + -2x = -1x
-9i + 3iy = -4 + -1x

Reorder the terms:
4 + -9i + 3iy + x = -4 + -1x + 4 + x

Reorder the terms:
4 + -9i + 3iy + x = -4 + 4 + -1x + x

Combine like terms: -4 + 4 = 0
4 + -9i + 3iy + x = 0 + -1x + x
4 + -9i + 3iy + x = -1x + x

Combine like terms: -1x + x = 0
4 + -9i + 3iy + x = 0

The solution to this equation could not be determined.