(i+1)(x+2iy)+i(x+iy)=1+2i

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Solution for (i+1)(x+2iy)+i(x+iy)=1+2i equation: 


Simplifying
(i + 1)(x + 2iy) + i(x + iy) = 1 + 2i

Reorder the terms:
(1 + i)(x + 2iy) + i(x + iy) = 1 + 2i

Reorder the terms:
(1 + i)(2iy + x) + i(x + iy) = 1 + 2i

Multiply (1 + i) * (2iy + x)
(1(2iy + x) + i(2iy + x)) + i(x + iy) = 1 + 2i
((2iy * 1 + x * 1) + i(2iy + x)) + i(x + iy) = 1 + 2i
((2iy + 1x) + i(2iy + x)) + i(x + iy) = 1 + 2i
(2iy + 1x + (2iy * i + x * i)) + i(x + iy) = 1 + 2i

Reorder the terms:
(2iy + 1x + (ix + 2i2y)) + i(x + iy) = 1 + 2i
(2iy + 1x + (ix + 2i2y)) + i(x + iy) = 1 + 2i

Reorder the terms:
(ix + 2iy + 2i2y + 1x) + i(x + iy) = 1 + 2i
(ix + 2iy + 2i2y + 1x) + i(x + iy) = 1 + 2i

Reorder the terms:
ix + 2iy + 2i2y + 1x + i(iy + x) = 1 + 2i
ix + 2iy + 2i2y + 1x + (iy * i + x * i) = 1 + 2i

Reorder the terms:
ix + 2iy + 2i2y + 1x + (ix + i2y) = 1 + 2i
ix + 2iy + 2i2y + 1x + (ix + i2y) = 1 + 2i

Reorder the terms:
ix + ix + 2iy + 2i2y + i2y + 1x = 1 + 2i

Combine like terms: ix + ix = 2ix
2ix + 2iy + 2i2y + i2y + 1x = 1 + 2i

Combine like terms: 2i2y + i2y = 3i2y
2ix + 2iy + 3i2y + 1x = 1 + 2i

Solving
2ix + 2iy + 3i2y + 1x = 1 + 2i

Solving for variable 'i'.

Reorder the terms:
-1 + -2i + 2ix + 2iy + 3i2y + 1x = 1 + 2i + -1 + -2i

Reorder the terms:
-1 + -2i + 2ix + 2iy + 3i2y + 1x = 1 + -1 + 2i + -2i

Combine like terms: 1 + -1 = 0
-1 + -2i + 2ix + 2iy + 3i2y + 1x = 0 + 2i + -2i
-1 + -2i + 2ix + 2iy + 3i2y + 1x = 2i + -2i

Combine like terms: 2i + -2i = 0
-1 + -2i + 2ix + 2iy + 3i2y + 1x = 0

The solution to this equation could not be determined.

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