20-(4+2i)(3-2i)=

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Solution for 20-(4+2i)(3-2i)= equation: 


Simplifying
20 + -1(4 + 2i)(3 + -2i) = 0

Multiply (4 + 2i) * (3 + -2i)
20 + -1(4(3 + -2i) + 2i * (3 + -2i)) = 0
20 + -1((3 * 4 + -2i * 4) + 2i * (3 + -2i)) = 0
20 + -1((12 + -8i) + 2i * (3 + -2i)) = 0
20 + -1(12 + -8i + (3 * 2i + -2i * 2i)) = 0
20 + -1(12 + -8i + (6i + -4i2)) = 0

Combine like terms: -8i + 6i = -2i
20 + -1(12 + -2i + -4i2) = 0
20 + (12 * -1 + -2i * -1 + -4i2 * -1) = 0
20 + (-12 + 2i + 4i2) = 0

Combine like terms: 20 + -12 = 8
8 + 2i + 4i2 = 0

Solving
8 + 2i + 4i2 = 0

Solving for variable 'i'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + i + 2i2)' equal to zero and attempt to solve:

Simplifying
4 + i + 2i2 = 0

Solving
4 + i + 2i2 = 0

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

Divide each side by '2'.
2 + 0.5i + i2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.5i + -2 + i2 = 0 + -2

Reorder the terms:
2 + -2 + 0.5i + i2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.5i + i2 = 0 + -2
0.5i + i2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.5i + i2 = -2

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.
0.5i + 0.25 + i2 = -2 + 0.25

Reorder the terms:
0.25 + 0.5i + i2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + 0.5i + i2 = -1.75

Factor a perfect square on the left side:
(i + 0.5)(i + 0.5) = -1.75

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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