(-5+3i)(-2+8i)=0

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Solution for (-5+3i)(-2+8i)=0 equation: 


Simplifying
(-5 + 3i)(-2 + 8i) = 0

Multiply (-5 + 3i) * (-2 + 8i)
(-5(-2 + 8i) + 3i * (-2 + 8i)) = 0
((-2 * -5 + 8i * -5) + 3i * (-2 + 8i)) = 0
((10 + -40i) + 3i * (-2 + 8i)) = 0
(10 + -40i + (-2 * 3i + 8i * 3i)) = 0
(10 + -40i + (-6i + 24i2)) = 0

Combine like terms: -40i + -6i = -46i
(10 + -46i + 24i2) = 0

Solving
10 + -46i + 24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -23i + 12i2) = 0

Factor a trinomial.
2((1 + -4i)(5 + -3i)) = 0

Ignore the factor 2.

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

Simplifying
1 + -4i = 0

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

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

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

Divide each side by '-4'.
i = 0.25

Simplifying
i = 0.25

Subproblem 2
Set the factor '(5 + -3i)' equal to zero and attempt to solve:

Simplifying
5 + -3i = 0

Solving
5 + -3i = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3i = 0 + -5
-3i = 0 + -5

Combine like terms: 0 + -5 = -5
-3i = -5

Divide each side by '-3'.
i = 1.666666667

Simplifying
i = 1.666666667
Solution
i = {0.25, 1.666666667}

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