116+12i=(8+6i)(8-8i)

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Solution for 116+12i=(8+6i)(8-8i) equation: 


Simplifying
116 + 12i = (8 + 6i)(8 + -8i)

Multiply (8 + 6i) * (8 + -8i)
116 + 12i = (8(8 + -8i) + 6i * (8 + -8i))
116 + 12i = ((8 * 8 + -8i * 8) + 6i * (8 + -8i))
116 + 12i = ((64 + -64i) + 6i * (8 + -8i))
116 + 12i = (64 + -64i + (8 * 6i + -8i * 6i))
116 + 12i = (64 + -64i + (48i + -48i2))

Combine like terms: -64i + 48i = -16i
116 + 12i = (64 + -16i + -48i2)

Solving
116 + 12i = 64 + -16i + -48i2

Solving for variable 'i'.

Reorder the terms:
116 + -64 + 12i + 16i + 48i2 = 64 + -16i + -48i2 + -64 + 16i + 48i2

Combine like terms: 116 + -64 = 52
52 + 12i + 16i + 48i2 = 64 + -16i + -48i2 + -64 + 16i + 48i2

Combine like terms: 12i + 16i = 28i
52 + 28i + 48i2 = 64 + -16i + -48i2 + -64 + 16i + 48i2

Reorder the terms:
52 + 28i + 48i2 = 64 + -64 + -16i + 16i + -48i2 + 48i2

Combine like terms: 64 + -64 = 0
52 + 28i + 48i2 = 0 + -16i + 16i + -48i2 + 48i2
52 + 28i + 48i2 = -16i + 16i + -48i2 + 48i2

Combine like terms: -16i + 16i = 0
52 + 28i + 48i2 = 0 + -48i2 + 48i2
52 + 28i + 48i2 = -48i2 + 48i2

Combine like terms: -48i2 + 48i2 = 0
52 + 28i + 48i2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(13 + 7i + 12i2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(13 + 7i + 12i2)' equal to zero and attempt to solve:

Simplifying
13 + 7i + 12i2 = 0

Solving
13 + 7i + 12i2 = 0

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
1.083333333 + 0.5833333333i + i2 = 0

Move the constant term to the right:

Add '-1.083333333' to each side of the equation.
1.083333333 + 0.5833333333i + -1.083333333 + i2 = 0 + -1.083333333

Reorder the terms:
1.083333333 + -1.083333333 + 0.5833333333i + i2 = 0 + -1.083333333

Combine like terms: 1.083333333 + -1.083333333 = 0.000000000
0.000000000 + 0.5833333333i + i2 = 0 + -1.083333333
0.5833333333i + i2 = 0 + -1.083333333

Combine like terms: 0 + -1.083333333 = -1.083333333
0.5833333333i + i2 = -1.083333333

The i term is 0.5833333333i.  Take half its coefficient (0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
0.5833333333i + 0.08506944446 + i2 = -1.083333333 + 0.08506944446

Reorder the terms:
0.08506944446 + 0.5833333333i + i2 = -1.083333333 + 0.08506944446

Combine like terms: -1.083333333 + 0.08506944446 = -0.99826388854
0.08506944446 + 0.5833333333i + i2 = -0.99826388854

Factor a perfect square on the left side:
(i + 0.2916666667)(i + 0.2916666667) = -0.99826388854

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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