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Simplifying (3 + I)(4 + 2i) = 0 Multiply (3 + I) * (4 + 2i) (3(4 + 2i) + I(4 + 2i)) = 0 ((4 * 3 + 2i * 3) + I(4 + 2i)) = 0 ((12 + 6i) + I(4 + 2i)) = 0 (12 + 6i + (4 * I + 2i * I)) = 0 (12 + 6i + (4I + 2iI)) = 0 Reorder the terms: (12 + 4I + 6i + 2iI) = 0 (12 + 4I + 6i + 2iI) = 0 Solving 12 + 4I + 6i + 2iI = 0 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 4I + 6i + -12 + 2iI = 0 + -12 Reorder the terms: 12 + -12 + 4I + 6i + 2iI = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 4I + 6i + 2iI = 0 + -12 4I + 6i + 2iI = 0 + -12 Combine like terms: 0 + -12 = -12 4I + 6i + 2iI = -12 Add '-6i' to each side of the equation. 4I + 6i + -6i + 2iI = -12 + -6i Combine like terms: 6i + -6i = 0 4I + 0 + 2iI = -12 + -6i 4I + 2iI = -12 + -6i Reorder the terms: 12 + 4I + 6i + 2iI = -12 + -6i + 12 + 6i Reorder the terms: 12 + 4I + 6i + 2iI = -12 + 12 + -6i + 6i Combine like terms: -12 + 12 = 0 12 + 4I + 6i + 2iI = 0 + -6i + 6i 12 + 4I + 6i + 2iI = -6i + 6i Combine like terms: -6i + 6i = 0 12 + 4I + 6i + 2iI = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 2I + 3i + iI) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 2I + 3i + iI)' equal to zero and attempt to solve: Simplifying 6 + 2I + 3i + iI = 0 Solving 6 + 2I + 3i + iI = 0 Move all terms containing I to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + 2I + 3i + -6 + iI = 0 + -6 Reorder the terms: 6 + -6 + 2I + 3i + iI = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 2I + 3i + iI = 0 + -6 2I + 3i + iI = 0 + -6 Combine like terms: 0 + -6 = -6 2I + 3i + iI = -6 Add '-3i' to each side of the equation. 2I + 3i + -3i + iI = -6 + -3i Combine like terms: 3i + -3i = 0 2I + 0 + iI = -6 + -3i 2I + iI = -6 + -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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