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Simplifying (2 + 4i)(4 + -1I) = 0 Multiply (2 + 4i) * (4 + -1I) (2(4 + -1I) + 4i * (4 + -1I)) = 0 ((4 * 2 + -1I * 2) + 4i * (4 + -1I)) = 0 ((8 + -2I) + 4i * (4 + -1I)) = 0 (8 + -2I + (4 * 4i + -1I * 4i)) = 0 (8 + -2I + (16i + -4iI)) = 0 (8 + -2I + 16i + -4iI) = 0 Solving 8 + -2I + 16i + -4iI = 0 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -2I + 16i + -8 + -4iI = 0 + -8 Reorder the terms: 8 + -8 + -2I + 16i + -4iI = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -2I + 16i + -4iI = 0 + -8 -2I + 16i + -4iI = 0 + -8 Combine like terms: 0 + -8 = -8 -2I + 16i + -4iI = -8 Add '-16i' to each side of the equation. -2I + 16i + -16i + -4iI = -8 + -16i Combine like terms: 16i + -16i = 0 -2I + 0 + -4iI = -8 + -16i -2I + -4iI = -8 + -16i Reorder the terms: 8 + -2I + 16i + -4iI = -8 + -16i + 8 + 16i Reorder the terms: 8 + -2I + 16i + -4iI = -8 + 8 + -16i + 16i Combine like terms: -8 + 8 = 0 8 + -2I + 16i + -4iI = 0 + -16i + 16i 8 + -2I + 16i + -4iI = -16i + 16i Combine like terms: -16i + 16i = 0 8 + -2I + 16i + -4iI = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -1I + 8i + -2iI) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1I + 8i + -2iI)' equal to zero and attempt to solve: Simplifying 4 + -1I + 8i + -2iI = 0 Solving 4 + -1I + 8i + -2iI = 0 Move all terms containing I to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -1I + 8i + -4 + -2iI = 0 + -4 Reorder the terms: 4 + -4 + -1I + 8i + -2iI = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1I + 8i + -2iI = 0 + -4 -1I + 8i + -2iI = 0 + -4 Combine like terms: 0 + -4 = -4 -1I + 8i + -2iI = -4 Add '-8i' to each side of the equation. -1I + 8i + -8i + -2iI = -4 + -8i Combine like terms: 8i + -8i = 0 -1I + 0 + -2iI = -4 + -8i -1I + -2iI = -4 + -8i 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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