(5+3i)(8+6i)=

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Solution for (5+3i)(8+6i)= equation: 


Simplifying
(5 + 3i)(8 + 6i) = 0

Multiply (5 + 3i) * (8 + 6i)
(5(8 + 6i) + 3i * (8 + 6i)) = 0
((8 * 5 + 6i * 5) + 3i * (8 + 6i)) = 0
((40 + 30i) + 3i * (8 + 6i)) = 0
(40 + 30i + (8 * 3i + 6i * 3i)) = 0
(40 + 30i + (24i + 18i2)) = 0

Combine like terms: 30i + 24i = 54i
(40 + 54i + 18i2) = 0

Solving
40 + 54i + 18i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 27i + 9i2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {-1.666666667, -1.333333333}

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