(7-3i)(8+4i)=64

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Solution for (7-3i)(8+4i)=64 equation: 


Simplifying
(7 + -3i)(8 + 4i) = 64

Multiply (7 + -3i) * (8 + 4i)
(7(8 + 4i) + -3i * (8 + 4i)) = 64
((8 * 7 + 4i * 7) + -3i * (8 + 4i)) = 64
((56 + 28i) + -3i * (8 + 4i)) = 64
(56 + 28i + (8 * -3i + 4i * -3i)) = 64
(56 + 28i + (-24i + -12i2)) = 64

Combine like terms: 28i + -24i = 4i
(56 + 4i + -12i2) = 64

Solving
56 + 4i + -12i2 = 64

Solving for variable 'i'.

Reorder the terms:
56 + -64 + 4i + -12i2 = 64 + -64

Combine like terms: 56 + -64 = -8
-8 + 4i + -12i2 = 64 + -64

Combine like terms: 64 + -64 = 0
-8 + 4i + -12i2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + i + -3i2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + i + -3i2)' equal to zero and attempt to solve:

Simplifying
-2 + i + -3i2 = 0

Solving
-2 + i + -3i2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
0.6666666667 + -0.3333333333i + i2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -0.3333333333i + -0.6666666667 + i2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -0.3333333333i + i2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -0.3333333333i + i2 = 0 + -0.6666666667
-0.3333333333i + i2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-0.3333333333i + i2 = -0.6666666667

The i term is i.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.3333333333i + 0.25 + i2 = -0.6666666667 + 0.25

Reorder the terms:
0.25 + -0.3333333333i + i2 = -0.6666666667 + 0.25

Combine like terms: -0.6666666667 + 0.25 = -0.4166666667
0.25 + -0.3333333333i + i2 = -0.4166666667

Factor a perfect square on the left side:
(i + 0.5)(i + 0.5) = -0.4166666667

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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