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Simplifying (4 + 3i)(-1 + -2i) = 0 Multiply (4 + 3i) * (-1 + -2i) (4(-1 + -2i) + 3i * (-1 + -2i)) = 0 ((-1 * 4 + -2i * 4) + 3i * (-1 + -2i)) = 0 ((-4 + -8i) + 3i * (-1 + -2i)) = 0 (-4 + -8i + (-1 * 3i + -2i * 3i)) = 0 (-4 + -8i + (-3i + -6i2)) = 0 Combine like terms: -8i + -3i = -11i (-4 + -11i + -6i2) = 0 Solving -4 + -11i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 11i + 6i2) = 0 Factor a trinomial. -1((4 + 3i)(1 + 2i)) = 0 Ignore the factor -1.Subproblem 1
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 = -1.333333333Subproblem 2
Set the factor '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Solution
i = {-1.333333333, -0.5}
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