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

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


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

Multiply (4 + 3i) * (8 + -2i)
(4(8 + -2i) + 3i * (8 + -2i)) = 0
((8 * 4 + -2i * 4) + 3i * (8 + -2i)) = 0
((32 + -8i) + 3i * (8 + -2i)) = 0
(32 + -8i + (8 * 3i + -2i * 3i)) = 0
(32 + -8i + (24i + -6i2)) = 0

Combine like terms: -8i + 24i = 16i
(32 + 16i + -6i2) = 0

Solving
32 + 16i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 8i + -3i2) = 0

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

Ignore the factor 2.

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

Simplifying
4 + -1i = 0

Solving
4 + -1i = 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 + -1i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1i = 0 + -4
-1i = 0 + -4

Combine like terms: 0 + -4 = -4
-1i = -4

Divide each side by '-1'.
i = 4

Simplifying
i = 4

Subproblem 2
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
Solution
i = {4, -1.333333333}

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