(2-4i)(6+6i)=

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Solution for (2-4i)(6+6i)= equation:


Simplifying
(2 + -4i)(6 + 6i) = 0

Multiply (2 + -4i) * (6 + 6i)
(2(6 + 6i) + -4i * (6 + 6i)) = 0
((6 * 2 + 6i * 2) + -4i * (6 + 6i)) = 0
((12 + 12i) + -4i * (6 + 6i)) = 0
(12 + 12i + (6 * -4i + 6i * -4i)) = 0
(12 + 12i + (-24i + -24i2)) = 0

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

Solving
12 + -12i + -24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '12'.
12(1 + -1i + -2i2) = 0

Factor a trinomial.
12((1 + -2i)(1 + i)) = 0

Ignore the factor 12.

Subproblem 1

Set the factor '(1 + -2i)' equal to zero and attempt to solve: Simplifying 1 + -2i = 0 Solving 1 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2i = 0 + -1 -2i = 0 + -1 Combine like terms: 0 + -1 = -1 -2i = -1 Divide each side by '-2'. i = 0.5 Simplifying i = 0.5

Subproblem 2

Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1

Solution

i = {0.5, -1}

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