(3-4i)(1-i)-(4-i)(4+i)=

Solution for (3-4i)(1-i)-(4-i)(4+i)= equation:

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

Multiply (3 + -4i) * (1 + -1i)
(3(1 + -1i) + -4i * (1 + -1i)) + -1(4 + -1i)(4 + i) = 0
((1 * 3 + -1i * 3) + -4i * (1 + -1i)) + -1(4 + -1i)(4 + i) = 0
((3 + -3i) + -4i * (1 + -1i)) + -1(4 + -1i)(4 + i) = 0
(3 + -3i + (1 * -4i + -1i * -4i)) + -1(4 + -1i)(4 + i) = 0
(3 + -3i + (-4i + 4i2)) + -1(4 + -1i)(4 + i) = 0

Combine like terms: -3i + -4i = -7i
(3 + -7i + 4i2) + -1(4 + -1i)(4 + i) = 0

Multiply (4 + -1i) * (4 + i)
3 + -7i + 4i2 + -1(4(4 + i) + -1i * (4 + i)) = 0
3 + -7i + 4i2 + -1((4 * 4 + i * 4) + -1i * (4 + i)) = 0
3 + -7i + 4i2 + -1((16 + 4i) + -1i * (4 + i)) = 0
3 + -7i + 4i2 + -1(16 + 4i + (4 * -1i + i * -1i)) = 0
3 + -7i + 4i2 + -1(16 + 4i + (-4i + -1i2)) = 0

Combine like terms: 4i + -4i = 0
3 + -7i + 4i2 + -1(16 + 0 + -1i2) = 0
3 + -7i + 4i2 + -1(16 + -1i2) = 0
3 + -7i + 4i2 + (16 * -1 + -1i2 * -1) = 0
3 + -7i + 4i2 + (-16 + 1i2) = 0

Reorder the terms:
3 + -16 + -7i + 4i2 + 1i2 = 0

Combine like terms: 3 + -16 = -13
-13 + -7i + 4i2 + 1i2 = 0

Combine like terms: 4i2 + 1i2 = 5i2
-13 + -7i + 5i2 = 0

Solving
-13 + -7i + 5i2 = 0

Solving for variable 'i'.

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

Divide each side by '5'.
-2.6 + -1.4i + i2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + -1.4i + 2.6 + i2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + -1.4i + i2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + -1.4i + i2 = 0 + 2.6
-1.4i + i2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
-1.4i + i2 = 2.6

The i term is -1.4i.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4i + 0.49 + i2 = 2.6 + 0.49

Reorder the terms:
0.49 + -1.4i + i2 = 2.6 + 0.49

Combine like terms: 2.6 + 0.49 = 3.09
0.49 + -1.4i + i2 = 3.09

Factor a perfect square on the left side:
(i + -0.7)(i + -0.7) = 3.09

Calculate the square root of the right side: 1.757839583

Break this problem into two subproblems by setting 
(i + -0.7) equal to 1.757839583 and -1.757839583.

Subproblem 1
i + -0.7 = 1.757839583

Simplifying
i + -0.7 = 1.757839583

Reorder the terms:
-0.7 + i = 1.757839583

Solving
-0.7 + i = 1.757839583

Solving for variable 'i'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + i = 1.757839583 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + i = 1.757839583 + 0.7
i = 1.757839583 + 0.7

Combine like terms: 1.757839583 + 0.7 = 2.457839583
i = 2.457839583

Simplifying
i = 2.457839583

Subproblem 2
i + -0.7 = -1.757839583

Simplifying
i + -0.7 = -1.757839583

Reorder the terms:
-0.7 + i = -1.757839583

Solving
-0.7 + i = -1.757839583

Solving for variable 'i'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + i = -1.757839583 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + i = -1.757839583 + 0.7
i = -1.757839583 + 0.7

Combine like terms: -1.757839583 + 0.7 = -1.057839583
i = -1.057839583

Simplifying
i = -1.057839583

Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {2.457839583, -1.057839583}