(8-3i)(4+3i)=0

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Solution for (8-3i)(4+3i)=0 equation: 


Simplifying
(8 + -3i)(4 + 3i) = 0

Multiply (8 + -3i) * (4 + 3i)
(8(4 + 3i) + -3i * (4 + 3i)) = 0
((4 * 8 + 3i * 8) + -3i * (4 + 3i)) = 0
((32 + 24i) + -3i * (4 + 3i)) = 0
(32 + 24i + (4 * -3i + 3i * -3i)) = 0
(32 + 24i + (-12i + -9i2)) = 0

Combine like terms: 24i + -12i = 12i
(32 + 12i + -9i2) = 0

Solving
32 + 12i + -9i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(8 + -3i)(4 + 3i) = 0


Subproblem 1
Set the factor '(8 + -3i)' equal to zero and attempt to solve:

Simplifying
8 + -3i = 0

Solving
8 + -3i = 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 + -3i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3i = 0 + -8
-3i = 0 + -8

Combine like terms: 0 + -8 = -8
-3i = -8

Divide each side by '-3'.
i = 2.666666667

Simplifying
i = 2.666666667

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 = {2.666666667, -1.333333333}

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