(x+1+i)(x+1-i)=0

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


Simplifying
(x + 1 + i)(x + 1 + -1i) = 0

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

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

Multiply (1 + i + x) * (1 + -1i + x)
(1(1 + -1i + x) + i(1 + -1i + x) + x(1 + -1i + x)) = 0
((1 * 1 + -1i * 1 + x * 1) + i(1 + -1i + x) + x(1 + -1i + x)) = 0
((1 + -1i + 1x) + i(1 + -1i + x) + x(1 + -1i + x)) = 0
(1 + -1i + 1x + (1 * i + -1i * i + x * i) + x(1 + -1i + x)) = 0

Reorder the terms:
(1 + -1i + 1x + (1i + ix + -1i2) + x(1 + -1i + x)) = 0
(1 + -1i + 1x + (1i + ix + -1i2) + x(1 + -1i + x)) = 0
(1 + -1i + 1x + 1i + ix + -1i2 + (1 * x + -1i * x + x * x)) = 0

Reorder the terms:
(1 + -1i + 1x + 1i + ix + -1i2 + (-1ix + 1x + x2)) = 0
(1 + -1i + 1x + 1i + ix + -1i2 + (-1ix + 1x + x2)) = 0

Reorder the terms:
(1 + -1i + 1i + ix + -1ix + -1i2 + 1x + 1x + x2) = 0

Combine like terms: -1i + 1i = 0
(1 + 0 + ix + -1ix + -1i2 + 1x + 1x + x2) = 0
(1 + ix + -1ix + -1i2 + 1x + 1x + x2) = 0

Combine like terms: ix + -1ix = 0
(1 + 0 + -1i2 + 1x + 1x + x2) = 0
(1 + -1i2 + 1x + 1x + x2) = 0

Combine like terms: 1x + 1x = 2x
(1 + -1i2 + 2x + x2) = 0

Solving
1 + -1i2 + 2x + x2 = 0

Solving for variable 'i'.

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

Add '-1' to each side of the equation.
1 + -1i2 + 2x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1i2 + 2x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1i2 + 2x + x2 = 0 + -1
-1i2 + 2x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1i2 + 2x + x2 = -1

Add '-2x' to each side of the equation.
-1i2 + 2x + -2x + x2 = -1 + -2x

Combine like terms: 2x + -2x = 0
-1i2 + 0 + x2 = -1 + -2x
-1i2 + x2 = -1 + -2x

Add '-1x2' to each side of the equation.
-1i2 + x2 + -1x2 = -1 + -2x + -1x2

Combine like terms: x2 + -1x2 = 0
-1i2 + 0 = -1 + -2x + -1x2
-1i2 = -1 + -2x + -1x2

Divide each side by '-1'.
i2 = 1 + 2x + x2

Simplifying
i2 = 1 + 2x + x2

Reorder the terms:
-1 + i2 + -2x + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Reorder the terms:
-1 + i2 + -2x + -1x2 = 1 + -1 + 2x + -2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-1 + i2 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2
-1 + i2 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-1 + i2 + -2x + -1x2 = 0 + x2 + -1x2
-1 + i2 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 + i2 + -2x + -1x2 = 0

The solution to this equation could not be determined.

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