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

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Solution for =(2-1i)(4+3i) equation: 


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

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

Combine like terms: 6i + -4i = 2i
0 = (8 + 2i + -3i2)

Solving
0 = 8 + 2i + -3i2

Solving for variable 'i'.

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

Reorder the terms:
-8 + -2i + 3i2 = 8 + -8 + 2i + -2i + -3i2 + 3i2

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

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

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

Factor a trinomial.
(-4 + -3i)(2 + -1i) = 0


Subproblem 1
Set the factor '(-4 + -3i)' equal to zero and attempt to solve:

Simplifying
-4 + -3i = 0

Solving
-4 + -3i = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3i = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3i = 0 + 4
-3i = 0 + 4

Combine like terms: 0 + 4 = 4
-3i = 4

Divide each side by '-3'.
i = -1.333333333

Simplifying
i = -1.333333333

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

Simplifying
2 + -1i = 0

Solving
2 + -1i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
i = 2

Simplifying
i = 2
Solution
i = {-1.333333333, 2}

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