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Simplifying (5 + 2i)(-6 + -6i) = 0 Multiply (5 + 2i) * (-6 + -6i) (5(-6 + -6i) + 2i * (-6 + -6i)) = 0 ((-6 * 5 + -6i * 5) + 2i * (-6 + -6i)) = 0 ((-30 + -30i) + 2i * (-6 + -6i)) = 0 (-30 + -30i + (-6 * 2i + -6i * 2i)) = 0 (-30 + -30i + (-12i + -12i2)) = 0 Combine like terms: -30i + -12i = -42i (-30 + -42i + -12i2) = 0 Solving -30 + -42i + -12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-6'. -6(5 + 7i + 2i2) = 0 Factor a trinomial. -6((5 + 2i)(1 + i)) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(5 + 2i)' equal to zero and attempt to solve: Simplifying 5 + 2i = 0 Solving 5 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2i = 0 + -5 2i = 0 + -5 Combine like terms: 0 + -5 = -5 2i = -5 Divide each side by '2'. i = -2.5 Simplifying i = -2.5Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 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 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {-2.5, -1}
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