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

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


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

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

Combine like terms: 5i + -24i = -19i
(40 + -19i + -3i2) = 0

Solving
40 + -19i + -3i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(5 + -3i)(8 + i) = 0


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 '(8 + i)' equal to zero and attempt to solve:

Simplifying
8 + i = 0

Solving
8 + i = 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 + i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + i = 0 + -8
i = 0 + -8

Combine like terms: 0 + -8 = -8
i = -8

Simplifying
i = -8
Solution
i = {1.666666667, -8}

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