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Simplifying (2 + -4i)(-7 + I) = 0 Multiply (2 + -4i) * (-7 + I) (2(-7 + I) + -4i * (-7 + I)) = 0 ((-7 * 2 + I * 2) + -4i * (-7 + I)) = 0 ((-14 + 2I) + -4i * (-7 + I)) = 0 (-14 + 2I + (-7 * -4i + I * -4i)) = 0 (-14 + 2I + (28i + -4iI)) = 0 (-14 + 2I + 28i + -4iI) = 0 Solving -14 + 2I + 28i + -4iI = 0 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 2I + 28i + 14 + -4iI = 0 + 14 Reorder the terms: -14 + 14 + 2I + 28i + -4iI = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2I + 28i + -4iI = 0 + 14 2I + 28i + -4iI = 0 + 14 Combine like terms: 0 + 14 = 14 2I + 28i + -4iI = 14 Add '-28i' to each side of the equation. 2I + 28i + -28i + -4iI = 14 + -28i Combine like terms: 28i + -28i = 0 2I + 0 + -4iI = 14 + -28i 2I + -4iI = 14 + -28i Reorder the terms: -14 + 2I + 28i + -4iI = 14 + -28i + -14 + 28i Reorder the terms: -14 + 2I + 28i + -4iI = 14 + -14 + -28i + 28i Combine like terms: 14 + -14 = 0 -14 + 2I + 28i + -4iI = 0 + -28i + 28i -14 + 2I + 28i + -4iI = -28i + 28i Combine like terms: -28i + 28i = 0 -14 + 2I + 28i + -4iI = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + I + 14i + -2iI) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + I + 14i + -2iI)' equal to zero and attempt to solve: Simplifying -7 + I + 14i + -2iI = 0 Solving -7 + I + 14i + -2iI = 0 Move all terms containing I to the left, all other terms to the right. Add '7' to each side of the equation. -7 + I + 14i + 7 + -2iI = 0 + 7 Reorder the terms: -7 + 7 + I + 14i + -2iI = 0 + 7 Combine like terms: -7 + 7 = 0 0 + I + 14i + -2iI = 0 + 7 I + 14i + -2iI = 0 + 7 Combine like terms: 0 + 7 = 7 I + 14i + -2iI = 7 Add '-14i' to each side of the equation. I + 14i + -14i + -2iI = 7 + -14i Combine like terms: 14i + -14i = 0 I + 0 + -2iI = 7 + -14i I + -2iI = 7 + -14i 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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