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Simplifying (6i)(2i)(2 + -6i) = 0 Remove parenthesis around (6i) 6i(2i)(2 + -6i) = 0 Remove parenthesis around (2i) 6i * 2i(2 + -6i) = 0 Reorder the terms for easier multiplication: 6 * 2i * i(2 + -6i) = 0 Multiply 6 * 2 12i * i(2 + -6i) = 0 Multiply i * i 12i2(2 + -6i) = 0 (2 * 12i2 + -6i * 12i2) = 0 (24i2 + -72i3) = 0 Solving 24i2 + -72i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '24i2'. 24i2(1 + -3i) = 0 Ignore the factor 24.Subproblem 1
Set the factor 'i2' equal to zero and attempt to solve: Simplifying i2 = 0 Solving i2 = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i2 = 0 Take the square root of each side: i = {0}Subproblem 2
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Solution
i = {0, 0.3333333333}
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