(-8+9i)(5-3i)=0

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Solution for (-8+9i)(5-3i)=0 equation: 


Simplifying
(-8 + 9i)(5 + -3i) = 0

Multiply (-8 + 9i) * (5 + -3i)
(-8(5 + -3i) + 9i * (5 + -3i)) = 0
((5 * -8 + -3i * -8) + 9i * (5 + -3i)) = 0
((-40 + 24i) + 9i * (5 + -3i)) = 0
(-40 + 24i + (5 * 9i + -3i * 9i)) = 0
(-40 + 24i + (45i + -27i2)) = 0

Combine like terms: 24i + 45i = 69i
(-40 + 69i + -27i2) = 0

Solving
-40 + 69i + -27i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-5 + 3i)(8 + -9i) = 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 + -9i)' equal to zero and attempt to solve:

Simplifying
8 + -9i = 0

Solving
8 + -9i = 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 + -9i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -9i = 0 + -8
-9i = 0 + -8

Combine like terms: 0 + -8 = -8
-9i = -8

Divide each side by '-9'.
i = 0.8888888889

Simplifying
i = 0.8888888889
Solution
i = {1.666666667, 0.8888888889}

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