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Simplifying (2 + -8i)(4 + I) = 0 Multiply (2 + -8i) * (4 + I) (2(4 + I) + -8i * (4 + I)) = 0 ((4 * 2 + I * 2) + -8i * (4 + I)) = 0 ((8 + 2I) + -8i * (4 + I)) = 0 (8 + 2I + (4 * -8i + I * -8i)) = 0 (8 + 2I + (-32i + -8iI)) = 0 (8 + 2I + -32i + -8iI) = 0 Solving 8 + 2I + -32i + -8iI = 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 + -32i + -8 + -8iI = 0 + -8 Reorder the terms: 8 + -8 + 2I + -32i + -8iI = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 2I + -32i + -8iI = 0 + -8 2I + -32i + -8iI = 0 + -8 Combine like terms: 0 + -8 = -8 2I + -32i + -8iI = -8 Add '32i' to each side of the equation. 2I + -32i + 32i + -8iI = -8 + 32i Combine like terms: -32i + 32i = 0 2I + 0 + -8iI = -8 + 32i 2I + -8iI = -8 + 32i Reorder the terms: 8 + 2I + -32i + -8iI = -8 + 32i + 8 + -32i Reorder the terms: 8 + 2I + -32i + -8iI = -8 + 8 + 32i + -32i Combine like terms: -8 + 8 = 0 8 + 2I + -32i + -8iI = 0 + 32i + -32i 8 + 2I + -32i + -8iI = 32i + -32i Combine like terms: 32i + -32i = 0 8 + 2I + -32i + -8iI = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + I + -16i + -4iI) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + I + -16i + -4iI)' equal to zero and attempt to solve: Simplifying 4 + I + -16i + -4iI = 0 Solving 4 + I + -16i + -4iI = 0 Move all terms containing I to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + I + -16i + -4 + -4iI = 0 + -4 Reorder the terms: 4 + -4 + I + -16i + -4iI = 0 + -4 Combine like terms: 4 + -4 = 0 0 + I + -16i + -4iI = 0 + -4 I + -16i + -4iI = 0 + -4 Combine like terms: 0 + -4 = -4 I + -16i + -4iI = -4 Add '16i' to each side of the equation. I + -16i + 16i + -4iI = -4 + 16i Combine like terms: -16i + 16i = 0 I + 0 + -4iI = -4 + 16i I + -4iI = -4 + 16i 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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