(X+y)+(x-y)i=3+i

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Solution for (X+y)+(x-y)i=3+i equation: 


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

Remove parenthesis around (X + y)
X + y + (x + -1y) * i = 3 + i

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

Reorder the terms:
X + ix + -1iy + y = 3 + i

Solving
X + ix + -1iy + y = 3 + i

Solving for variable 'X'.

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

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

Reorder the terms:
X + ix + -1ix + -1iy + y = 3 + i + -1ix

Combine like terms: ix + -1ix = 0
X + 0 + -1iy + y = 3 + i + -1ix
X + -1iy + y = 3 + i + -1ix

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

Combine like terms: -1iy + iy = 0
X + 0 + y = 3 + i + -1ix + iy
X + y = 3 + i + -1ix + iy

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

Combine like terms: y + -1y = 0
X + 0 = 3 + i + -1ix + iy + -1y
X = 3 + i + -1ix + iy + -1y

Simplifying
X = 3 + i + -1ix + iy + -1y

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