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Simplifying (-3 + 2i)(-6 + -8i) = 0 Multiply (-3 + 2i) * (-6 + -8i) (-3(-6 + -8i) + 2i * (-6 + -8i)) = 0 ((-6 * -3 + -8i * -3) + 2i * (-6 + -8i)) = 0 ((18 + 24i) + 2i * (-6 + -8i)) = 0 (18 + 24i + (-6 * 2i + -8i * 2i)) = 0 (18 + 24i + (-12i + -16i2)) = 0 Combine like terms: 24i + -12i = 12i (18 + 12i + -16i2) = 0 Solving 18 + 12i + -16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 6i + -8i2) = 0 Factor a trinomial. 2((3 + -2i)(3 + 4i)) = 0 Ignore the factor 2.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 '(3 + 4i)' equal to zero and attempt to solve: Simplifying 3 + 4i = 0 Solving 3 + 4i = 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 + 4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4i = 0 + -3 4i = 0 + -3 Combine like terms: 0 + -3 = -3 4i = -3 Divide each side by '4'. i = -0.75 Simplifying i = -0.75Solution
i = {1.5, -0.75}
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