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Simplifying (10 + -1I)(2 + 4i) = 0 Multiply (10 + -1I) * (2 + 4i) (10(2 + 4i) + -1I * (2 + 4i)) = 0 ((2 * 10 + 4i * 10) + -1I * (2 + 4i)) = 0 ((20 + 40i) + -1I * (2 + 4i)) = 0 (20 + 40i + (2 * -1I + 4i * -1I)) = 0 (20 + 40i + (-2I + -4iI)) = 0 Reorder the terms: (20 + -2I + 40i + -4iI) = 0 (20 + -2I + 40i + -4iI) = 0 Solving 20 + -2I + 40i + -4iI = 0 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -2I + 40i + -20 + -4iI = 0 + -20 Reorder the terms: 20 + -20 + -2I + 40i + -4iI = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -2I + 40i + -4iI = 0 + -20 -2I + 40i + -4iI = 0 + -20 Combine like terms: 0 + -20 = -20 -2I + 40i + -4iI = -20 Add '-40i' to each side of the equation. -2I + 40i + -40i + -4iI = -20 + -40i Combine like terms: 40i + -40i = 0 -2I + 0 + -4iI = -20 + -40i -2I + -4iI = -20 + -40i Reorder the terms: 20 + -2I + 40i + -4iI = -20 + -40i + 20 + 40i Reorder the terms: 20 + -2I + 40i + -4iI = -20 + 20 + -40i + 40i Combine like terms: -20 + 20 = 0 20 + -2I + 40i + -4iI = 0 + -40i + 40i 20 + -2I + 40i + -4iI = -40i + 40i Combine like terms: -40i + 40i = 0 20 + -2I + 40i + -4iI = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -1I + 20i + -2iI) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + -1I + 20i + -2iI)' equal to zero and attempt to solve: Simplifying 10 + -1I + 20i + -2iI = 0 Solving 10 + -1I + 20i + -2iI = 0 Move all terms containing I to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -1I + 20i + -10 + -2iI = 0 + -10 Reorder the terms: 10 + -10 + -1I + 20i + -2iI = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1I + 20i + -2iI = 0 + -10 -1I + 20i + -2iI = 0 + -10 Combine like terms: 0 + -10 = -10 -1I + 20i + -2iI = -10 Add '-20i' to each side of the equation. -1I + 20i + -20i + -2iI = -10 + -20i Combine like terms: 20i + -20i = 0 -1I + 0 + -2iI = -10 + -20i -1I + -2iI = -10 + -20i 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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