(3+2i)(2-2i)=19+4

Solution for (3+2i)(2-2i)=19+4 equation:

Simplifying
(3 + 2i)(2 + -2i) = 19 + 4

Multiply (3 + 2i) * (2 + -2i)
(3(2 + -2i) + 2i * (2 + -2i)) = 19 + 4
((2 * 3 + -2i * 3) + 2i * (2 + -2i)) = 19 + 4
((6 + -6i) + 2i * (2 + -2i)) = 19 + 4
(6 + -6i + (2 * 2i + -2i * 2i)) = 19 + 4
(6 + -6i + (4i + -4i2)) = 19 + 4

Combine like terms: -6i + 4i = -2i
(6 + -2i + -4i2) = 19 + 4

Combine like terms: 19 + 4 = 23
6 + -2i + -4i2 = 23

Solving
6 + -2i + -4i2 = 23

Solving for variable 'i'.

Reorder the terms:
6 + -23 + -2i + -4i2 = 23 + -23

Combine like terms: 6 + -23 = -17
-17 + -2i + -4i2 = 23 + -23

Combine like terms: 23 + -23 = 0
-17 + -2i + -4i2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(17 + 2i + 4i2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(17 + 2i + 4i2)' equal to zero and attempt to solve:

Simplifying
17 + 2i + 4i2 = 0

Solving
17 + 2i + 4i2 = 0

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

Divide each side by '4'.
4.25 + 0.5i + i2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + 0.5i + -4.25 + i2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + 0.5i + i2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + 0.5i + i2 = 0 + -4.25
0.5i + i2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
0.5i + i2 = -4.25

The i term is 0.5i.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5i + 0.0625 + i2 = -4.25 + 0.0625

Reorder the terms:
0.0625 + 0.5i + i2 = -4.25 + 0.0625

Combine like terms: -4.25 + 0.0625 = -4.1875
0.0625 + 0.5i + i2 = -4.1875

Factor a perfect square on the left side:
(i + 0.25)(i + 0.25) = -4.1875

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.