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Simplifying (18 + -9i)(2 + I) = 0 Multiply (18 + -9i) * (2 + I) (18(2 + I) + -9i * (2 + I)) = 0 ((2 * 18 + I * 18) + -9i * (2 + I)) = 0 ((36 + 18I) + -9i * (2 + I)) = 0 (36 + 18I + (2 * -9i + I * -9i)) = 0 (36 + 18I + (-18i + -9iI)) = 0 (36 + 18I + -18i + -9iI) = 0 Solving 36 + 18I + -18i + -9iI = 0 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + 18I + -18i + -36 + -9iI = 0 + -36 Reorder the terms: 36 + -36 + 18I + -18i + -9iI = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 18I + -18i + -9iI = 0 + -36 18I + -18i + -9iI = 0 + -36 Combine like terms: 0 + -36 = -36 18I + -18i + -9iI = -36 Add '18i' to each side of the equation. 18I + -18i + 18i + -9iI = -36 + 18i Combine like terms: -18i + 18i = 0 18I + 0 + -9iI = -36 + 18i 18I + -9iI = -36 + 18i Reorder the terms: 36 + 18I + -18i + -9iI = -36 + 18i + 36 + -18i Reorder the terms: 36 + 18I + -18i + -9iI = -36 + 36 + 18i + -18i Combine like terms: -36 + 36 = 0 36 + 18I + -18i + -9iI = 0 + 18i + -18i 36 + 18I + -18i + -9iI = 18i + -18i Combine like terms: 18i + -18i = 0 36 + 18I + -18i + -9iI = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(4 + 2I + -2i + -1iI) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(4 + 2I + -2i + -1iI)' equal to zero and attempt to solve: Simplifying 4 + 2I + -2i + -1iI = 0 Solving 4 + 2I + -2i + -1iI = 0 Move all terms containing I to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 2I + -2i + -4 + -1iI = 0 + -4 Reorder the terms: 4 + -4 + 2I + -2i + -1iI = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2I + -2i + -1iI = 0 + -4 2I + -2i + -1iI = 0 + -4 Combine like terms: 0 + -4 = -4 2I + -2i + -1iI = -4 Add '2i' to each side of the equation. 2I + -2i + 2i + -1iI = -4 + 2i Combine like terms: -2i + 2i = 0 2I + 0 + -1iI = -4 + 2i 2I + -1iI = -4 + 2i 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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