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Simplifying (-4 + -3i)(3 + 2i) = 0 Multiply (-4 + -3i) * (3 + 2i) (-4(3 + 2i) + -3i * (3 + 2i)) = 0 ((3 * -4 + 2i * -4) + -3i * (3 + 2i)) = 0 ((-12 + -8i) + -3i * (3 + 2i)) = 0 (-12 + -8i + (3 * -3i + 2i * -3i)) = 0 (-12 + -8i + (-9i + -6i2)) = 0 Combine like terms: -8i + -9i = -17i (-12 + -17i + -6i2) = 0 Solving -12 + -17i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 17i + 6i2) = 0 Factor a trinomial. -1((3 + 2i)(4 + 3i)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Subproblem 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 = {-1.5, -1.333333333}
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