(9-3i)(8+i)=0

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Solution for (9-3i)(8+i)=0 equation: 


Simplifying
(9 + -3i)(8 + i) = 0

Multiply (9 + -3i) * (8 + i)
(9(8 + i) + -3i * (8 + i)) = 0
((8 * 9 + i * 9) + -3i * (8 + i)) = 0
((72 + 9i) + -3i * (8 + i)) = 0
(72 + 9i + (8 * -3i + i * -3i)) = 0
(72 + 9i + (-24i + -3i2)) = 0

Combine like terms: 9i + -24i = -15i
(72 + -15i + -3i2) = 0

Solving
72 + -15i + -3i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + -5i + -1i2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + -1i)' equal to zero and attempt to solve:

Simplifying
3 + -1i = 0

Solving
3 + -1i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i = 0 + -3
-1i = 0 + -3

Combine like terms: 0 + -3 = -3
-1i = -3

Divide each side by '-1'.
i = 3

Simplifying
i = 3

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 = {3, -8}

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