(X+1+2i)(x+1+2i)=0

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Solution for (X+1+2i)(x+1+2i)=0 equation: 


Simplifying
(X + 1 + 2i)(x + 1 + 2i) = 0

Reorder the terms:
(1 + X + 2i)(x + 1 + 2i) = 0

Reorder the terms:
(1 + X + 2i)(1 + 2i + x) = 0

Multiply (1 + X + 2i) * (1 + 2i + x)
(1(1 + 2i + x) + X(1 + 2i + x) + 2i * (1 + 2i + x)) = 0
((1 * 1 + 2i * 1 + x * 1) + X(1 + 2i + x) + 2i * (1 + 2i + x)) = 0
((1 + 2i + 1x) + X(1 + 2i + x) + 2i * (1 + 2i + x)) = 0
(1 + 2i + 1x + (1 * X + 2i * X + x * X) + 2i * (1 + 2i + x)) = 0
(1 + 2i + 1x + (1X + 2iX + xX) + 2i * (1 + 2i + x)) = 0
(1 + 2i + 1x + 1X + 2iX + xX + (1 * 2i + 2i * 2i + x * 2i)) = 0

Reorder the terms:
(1 + 2i + 1x + 1X + 2iX + xX + (2i + 2ix + 4i2)) = 0
(1 + 2i + 1x + 1X + 2iX + xX + (2i + 2ix + 4i2)) = 0

Reorder the terms:
(1 + 1X + 2i + 2i + 2iX + 2ix + 4i2 + 1x + xX) = 0

Combine like terms: 2i + 2i = 4i
(1 + 1X + 4i + 2iX + 2ix + 4i2 + 1x + xX) = 0

Solving
1 + 1X + 4i + 2iX + 2ix + 4i2 + 1x + xX = 0

Solving for variable 'X'.

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

Add '-1' to each side of the equation.
1 + 1X + 4i + 2iX + 2ix + 4i2 + 1x + -1 + xX = 0 + -1

Reorder the terms:
1 + -1 + 1X + 4i + 2iX + 2ix + 4i2 + 1x + xX = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1X + 4i + 2iX + 2ix + 4i2 + 1x + xX = 0 + -1
1X + 4i + 2iX + 2ix + 4i2 + 1x + xX = 0 + -1

Combine like terms: 0 + -1 = -1
1X + 4i + 2iX + 2ix + 4i2 + 1x + xX = -1

Add '-4i' to each side of the equation.
1X + 4i + 2iX + 2ix + 4i2 + 1x + -4i + xX = -1 + -4i

Reorder the terms:
1X + 4i + -4i + 2iX + 2ix + 4i2 + 1x + xX = -1 + -4i

Combine like terms: 4i + -4i = 0
1X + 0 + 2iX + 2ix + 4i2 + 1x + xX = -1 + -4i
1X + 2iX + 2ix + 4i2 + 1x + xX = -1 + -4i

Add '-2ix' to each side of the equation.
1X + 2iX + 2ix + 4i2 + 1x + -2ix + xX = -1 + -4i + -2ix

Reorder the terms:
1X + 2iX + 2ix + -2ix + 4i2 + 1x + xX = -1 + -4i + -2ix

Combine like terms: 2ix + -2ix = 0
1X + 2iX + 0 + 4i2 + 1x + xX = -1 + -4i + -2ix
1X + 2iX + 4i2 + 1x + xX = -1 + -4i + -2ix

Add '-4i2' to each side of the equation.
1X + 2iX + 4i2 + 1x + -4i2 + xX = -1 + -4i + -2ix + -4i2

Reorder the terms:
1X + 2iX + 4i2 + -4i2 + 1x + xX = -1 + -4i + -2ix + -4i2

Combine like terms: 4i2 + -4i2 = 0
1X + 2iX + 0 + 1x + xX = -1 + -4i + -2ix + -4i2
1X + 2iX + 1x + xX = -1 + -4i + -2ix + -4i2

Add '-1x' to each side of the equation.
1X + 2iX + 1x + -1x + xX = -1 + -4i + -2ix + -4i2 + -1x

Combine like terms: 1x + -1x = 0
1X + 2iX + 0 + xX = -1 + -4i + -2ix + -4i2 + -1x
1X + 2iX + xX = -1 + -4i + -2ix + -4i2 + -1x

Reorder the terms:
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = -1 + -4i + -2ix + -4i2 + -1x + 1 + 4i + 2ix + 4i2 + x

Reorder the terms:
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = -1 + 1 + -4i + 4i + -2ix + 2ix + -4i2 + 4i2 + -1x + x

Combine like terms: -1 + 1 = 0
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = 0 + -4i + 4i + -2ix + 2ix + -4i2 + 4i2 + -1x + x
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = -4i + 4i + -2ix + 2ix + -4i2 + 4i2 + -1x + x

Combine like terms: -4i + 4i = 0
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = 0 + -2ix + 2ix + -4i2 + 4i2 + -1x + x
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = -2ix + 2ix + -4i2 + 4i2 + -1x + x

Combine like terms: -2ix + 2ix = 0
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = 0 + -4i2 + 4i2 + -1x + x
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = -4i2 + 4i2 + -1x + x

Combine like terms: -4i2 + 4i2 = 0
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = 0 + -1x + x
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = -1x + x

Combine like terms: -1x + x = 0
1 + 1X + 4i + 2iX + 2ix + 4i2 + x + xX = 0

The solution to this equation could not be determined.

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