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Simplifying (-6 + -5i)(1 + 3i) = 0 Multiply (-6 + -5i) * (1 + 3i) (-6(1 + 3i) + -5i * (1 + 3i)) = 0 ((1 * -6 + 3i * -6) + -5i * (1 + 3i)) = 0 ((-6 + -18i) + -5i * (1 + 3i)) = 0 (-6 + -18i + (1 * -5i + 3i * -5i)) = 0 (-6 + -18i + (-5i + -15i2)) = 0 Combine like terms: -18i + -5i = -23i (-6 + -23i + -15i2) = 0 Solving -6 + -23i + -15i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 23i + 15i2) = 0 Factor a trinomial. -1((6 + 5i)(1 + 3i)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 5i)' equal to zero and attempt to solve: Simplifying 6 + 5i = 0 Solving 6 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5i = 0 + -6 5i = 0 + -6 Combine like terms: 0 + -6 = -6 5i = -6 Divide each side by '5'. i = -1.2 Simplifying i = -1.2Subproblem 2
Set the factor '(1 + 3i)' equal to zero and attempt to solve: Simplifying 1 + 3i = 0 Solving 1 + 3i = 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 + 3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3i = 0 + -1 3i = 0 + -1 Combine like terms: 0 + -1 = -1 3i = -1 Divide each side by '3'. i = -0.3333333333 Simplifying i = -0.3333333333Solution
i = {-1.2, -0.3333333333}
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