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Simplifying (-12 + 3i)(4 + -3i) = 0 Multiply (-12 + 3i) * (4 + -3i) (-12(4 + -3i) + 3i * (4 + -3i)) = 0 ((4 * -12 + -3i * -12) + 3i * (4 + -3i)) = 0 ((-48 + 36i) + 3i * (4 + -3i)) = 0 (-48 + 36i + (4 * 3i + -3i * 3i)) = 0 (-48 + 36i + (12i + -9i2)) = 0 Combine like terms: 36i + 12i = 48i (-48 + 48i + -9i2) = 0 Solving -48 + 48i + -9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(-16 + 16i + -3i2) = 0 Factor a trinomial. 3((-4 + i)(4 + -3i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + i)' equal to zero and attempt to solve: Simplifying -4 + i = 0 Solving -4 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + i = 0 + 4 i = 0 + 4 Combine like terms: 0 + 4 = 4 i = 4 Simplifying i = 4Subproblem 2
Set the factor '(4 + -3i)' equal to zero and attempt to solve: Simplifying 4 + -3i = 0 Solving 4 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3i = 0 + -4 -3i = 0 + -4 Combine like terms: 0 + -4 = -4 -3i = -4 Divide each side by '-3'. i = 1.333333333 Simplifying i = 1.333333333Solution
i = {4, 1.333333333}
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