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

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


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

Multiply (5 + 3i) * (2 + -3i)
(5(2 + -3i) + 3i * (2 + -3i)) = 0
((2 * 5 + -3i * 5) + 3i * (2 + -3i)) = 0
((10 + -15i) + 3i * (2 + -3i)) = 0
(10 + -15i + (2 * 3i + -3i * 3i)) = 0
(10 + -15i + (6i + -9i2)) = 0

Combine like terms: -15i + 6i = -9i
(10 + -9i + -9i2) = 0

Solving
10 + -9i + -9i2 = 0

Solving for variable 'i'.

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


Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve:

Simplifying
2 + -3i = 0

Solving
2 + -3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667

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 = {0.6666666667, -1.666666667}

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