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

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


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

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

Combine like terms: -3i + -8i = -11i
(12 + -11i + 2i2) + -1(2 + -1i)(2 + i) = 0

Multiply (2 + -1i) * (2 + i)
12 + -11i + 2i2 + -1(2(2 + i) + -1i * (2 + i)) = 0
12 + -11i + 2i2 + -1((2 * 2 + i * 2) + -1i * (2 + i)) = 0
12 + -11i + 2i2 + -1((4 + 2i) + -1i * (2 + i)) = 0
12 + -11i + 2i2 + -1(4 + 2i + (2 * -1i + i * -1i)) = 0
12 + -11i + 2i2 + -1(4 + 2i + (-2i + -1i2)) = 0

Combine like terms: 2i + -2i = 0
12 + -11i + 2i2 + -1(4 + 0 + -1i2) = 0
12 + -11i + 2i2 + -1(4 + -1i2) = 0
12 + -11i + 2i2 + (4 * -1 + -1i2 * -1) = 0
12 + -11i + 2i2 + (-4 + 1i2) = 0

Reorder the terms:
12 + -4 + -11i + 2i2 + 1i2 = 0

Combine like terms: 12 + -4 = 8
8 + -11i + 2i2 + 1i2 = 0

Combine like terms: 2i2 + 1i2 = 3i2
8 + -11i + 3i2 = 0

Solving
8 + -11i + 3i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(1 + -1i)(8 + -3i) = 0


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

Simplifying
1 + -1i = 0

Solving
1 + -1i = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1i = 0 + -1
-1i = 0 + -1

Combine like terms: 0 + -1 = -1
-1i = -1

Divide each side by '-1'.
i = 1

Simplifying
i = 1

Subproblem 2
Set the factor '(8 + -3i)' equal to zero and attempt to solve:

Simplifying
8 + -3i = 0

Solving
8 + -3i = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3i = 0 + -8
-3i = 0 + -8

Combine like terms: 0 + -8 = -8
-3i = -8

Divide each side by '-3'.
i = 2.666666667

Simplifying
i = 2.666666667
Solution
i = {1, 2.666666667}

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