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Simplifying (-2 + -6i)(1 + I) = 0 Multiply (-2 + -6i) * (1 + I) (-2(1 + I) + -6i * (1 + I)) = 0 ((1 * -2 + I * -2) + -6i * (1 + I)) = 0 ((-2 + -2I) + -6i * (1 + I)) = 0 (-2 + -2I + (1 * -6i + I * -6i)) = 0 (-2 + -2I + (-6i + -6iI)) = 0 (-2 + -2I + -6i + -6iI) = 0 Solving -2 + -2I + -6i + -6iI = 0 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -2I + -6i + 2 + -6iI = 0 + 2 Reorder the terms: -2 + 2 + -2I + -6i + -6iI = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2I + -6i + -6iI = 0 + 2 -2I + -6i + -6iI = 0 + 2 Combine like terms: 0 + 2 = 2 -2I + -6i + -6iI = 2 Add '6i' to each side of the equation. -2I + -6i + 6i + -6iI = 2 + 6i Combine like terms: -6i + 6i = 0 -2I + 0 + -6iI = 2 + 6i -2I + -6iI = 2 + 6i Reorder the terms: -2 + -2I + -6i + -6iI = 2 + 6i + -2 + -6i Reorder the terms: -2 + -2I + -6i + -6iI = 2 + -2 + 6i + -6i Combine like terms: 2 + -2 = 0 -2 + -2I + -6i + -6iI = 0 + 6i + -6i -2 + -2I + -6i + -6iI = 6i + -6i Combine like terms: 6i + -6i = 0 -2 + -2I + -6i + -6iI = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(1 + I + 3i + 3iI) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(1 + I + 3i + 3iI)' equal to zero and attempt to solve: Simplifying 1 + I + 3i + 3iI = 0 Solving 1 + I + 3i + 3iI = 0 Move all terms containing I to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + I + 3i + -1 + 3iI = 0 + -1 Reorder the terms: 1 + -1 + I + 3i + 3iI = 0 + -1 Combine like terms: 1 + -1 = 0 0 + I + 3i + 3iI = 0 + -1 I + 3i + 3iI = 0 + -1 Combine like terms: 0 + -1 = -1 I + 3i + 3iI = -1 Add '-3i' to each side of the equation. I + 3i + -3i + 3iI = -1 + -3i Combine like terms: 3i + -3i = 0 I + 0 + 3iI = -1 + -3i I + 3iI = -1 + -3i The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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