(4-3i)(-4+6i)=

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Solution for (4-3i)(-4+6i)= equation: 


Simplifying
(4 + -3i)(-4 + 6i) = 0

Multiply (4 + -3i) * (-4 + 6i)
(4(-4 + 6i) + -3i * (-4 + 6i)) = 0
((-4 * 4 + 6i * 4) + -3i * (-4 + 6i)) = 0
((-16 + 24i) + -3i * (-4 + 6i)) = 0
(-16 + 24i + (-4 * -3i + 6i * -3i)) = 0
(-16 + 24i + (12i + -18i2)) = 0

Combine like terms: 24i + 12i = 36i
(-16 + 36i + -18i2) = 0

Solving
-16 + 36i + -18i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 18i + -9i2) = 0

Factor a trinomial.
2((-4 + 3i)(2 + -3i)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
i = {1.333333333, 0.6666666667}

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