(x+4-i)(x+4+i)=y

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Solution for (x+4-i)(x+4+i)=y equation: 


Simplifying
(x + 4 + -1i)(x + 4 + i) = y

Reorder the terms:
(4 + -1i + x)(x + 4 + i) = y

Reorder the terms:
(4 + -1i + x)(4 + i + x) = y

Multiply (4 + -1i + x) * (4 + i + x)
(4(4 + i + x) + -1i * (4 + i + x) + x(4 + i + x)) = y
((4 * 4 + i * 4 + x * 4) + -1i * (4 + i + x) + x(4 + i + x)) = y
((16 + 4i + 4x) + -1i * (4 + i + x) + x(4 + i + x)) = y
(16 + 4i + 4x + (4 * -1i + i * -1i + x * -1i) + x(4 + i + x)) = y

Reorder the terms:
(16 + 4i + 4x + (-4i + -1ix + -1i2) + x(4 + i + x)) = y
(16 + 4i + 4x + (-4i + -1ix + -1i2) + x(4 + i + x)) = y
(16 + 4i + 4x + -4i + -1ix + -1i2 + (4 * x + i * x + x * x)) = y

Reorder the terms:
(16 + 4i + 4x + -4i + -1ix + -1i2 + (ix + 4x + x2)) = y
(16 + 4i + 4x + -4i + -1ix + -1i2 + (ix + 4x + x2)) = y

Reorder the terms:
(16 + 4i + -4i + -1ix + ix + -1i2 + 4x + 4x + x2) = y

Combine like terms: 4i + -4i = 0
(16 + 0 + -1ix + ix + -1i2 + 4x + 4x + x2) = y
(16 + -1ix + ix + -1i2 + 4x + 4x + x2) = y

Combine like terms: -1ix + ix = 0
(16 + 0 + -1i2 + 4x + 4x + x2) = y
(16 + -1i2 + 4x + 4x + x2) = y

Combine like terms: 4x + 4x = 8x
(16 + -1i2 + 8x + x2) = y

Solving
16 + -1i2 + 8x + x2 = y

Solving for variable 'i'.

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

Add '-16' to each side of the equation.
16 + -1i2 + 8x + -16 + x2 = -16 + y

Reorder the terms:
16 + -16 + -1i2 + 8x + x2 = -16 + y

Combine like terms: 16 + -16 = 0
0 + -1i2 + 8x + x2 = -16 + y
-1i2 + 8x + x2 = -16 + y

Add '-8x' to each side of the equation.
-1i2 + 8x + -8x + x2 = -16 + -8x + y

Combine like terms: 8x + -8x = 0
-1i2 + 0 + x2 = -16 + -8x + y
-1i2 + x2 = -16 + -8x + y

Add '-1x2' to each side of the equation.
-1i2 + x2 + -1x2 = -16 + -8x + -1x2 + y

Combine like terms: x2 + -1x2 = 0
-1i2 + 0 = -16 + -8x + -1x2 + y
-1i2 = -16 + -8x + -1x2 + y

Divide each side by '-1'.
i2 = 16 + 8x + x2 + -1y

Simplifying
i2 = 16 + 8x + x2 + -1y

Reorder the terms:
-16 + i2 + -8x + -1x2 + y = 16 + 8x + x2 + -1y + -16 + -8x + -1x2 + y

Reorder the terms:
-16 + i2 + -8x + -1x2 + y = 16 + -16 + 8x + -8x + x2 + -1x2 + -1y + y

Combine like terms: 16 + -16 = 0
-16 + i2 + -8x + -1x2 + y = 0 + 8x + -8x + x2 + -1x2 + -1y + y
-16 + i2 + -8x + -1x2 + y = 8x + -8x + x2 + -1x2 + -1y + y

Combine like terms: 8x + -8x = 0
-16 + i2 + -8x + -1x2 + y = 0 + x2 + -1x2 + -1y + y
-16 + i2 + -8x + -1x2 + y = x2 + -1x2 + -1y + y

Combine like terms: x2 + -1x2 = 0
-16 + i2 + -8x + -1x2 + y = 0 + -1y + y
-16 + i2 + -8x + -1x2 + y = -1y + y

Combine like terms: -1y + y = 0
-16 + i2 + -8x + -1x2 + y = 0

The solution to this equation could not be determined.

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