(8+3i)(4-2i)=0

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Solution for (8+3i)(4-2i)=0 equation: 


Simplifying
(8 + 3i)(4 + -2i) = 0

Multiply (8 + 3i) * (4 + -2i)
(8(4 + -2i) + 3i * (4 + -2i)) = 0
((4 * 8 + -2i * 8) + 3i * (4 + -2i)) = 0
((32 + -16i) + 3i * (4 + -2i)) = 0
(32 + -16i + (4 * 3i + -2i * 3i)) = 0
(32 + -16i + (12i + -6i2)) = 0

Combine like terms: -16i + 12i = -4i
(32 + -4i + -6i2) = 0

Solving
32 + -4i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -2i + -3i2) = 0

Factor a trinomial.
2((2 + -1i)(8 + 3i)) = 0

Ignore the factor 2.

Subproblem 1
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

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 = {2, -2.666666667}

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