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Simplifying (-2i)(4i) + (8i)(2 + 3i) = 0 Remove parenthesis around (-2i) -2i(4i) + (8i)(2 + 3i) = 0 Remove parenthesis around (4i) -2i * 4i + (8i)(2 + 3i) = 0 Reorder the terms for easier multiplication: -2 * 4i * i + (8i)(2 + 3i) = 0 Multiply -2 * 4 -8i * i + (8i)(2 + 3i) = 0 Multiply i * i -8i2 + (8i)(2 + 3i) = 0 Remove parenthesis around (8i) -8i2 + 8i(2 + 3i) = 0 -8i2 + (2 * 8i + 3i * 8i) = 0 -8i2 + (16i + 24i2) = 0 Reorder the terms: 16i + -8i2 + 24i2 = 0 Combine like terms: -8i2 + 24i2 = 16i2 16i + 16i2 = 0 Solving 16i + 16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '16i'. 16i(1 + i) = 0 Ignore the factor 16.Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 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 = -1Solution
i = {0, -1}
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