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Simplifying (-4 + -8i)(-3 + -4i) = 0 Multiply (-4 + -8i) * (-3 + -4i) (-4(-3 + -4i) + -8i * (-3 + -4i)) = 0 ((-3 * -4 + -4i * -4) + -8i * (-3 + -4i)) = 0 ((12 + 16i) + -8i * (-3 + -4i)) = 0 (12 + 16i + (-3 * -8i + -4i * -8i)) = 0 (12 + 16i + (24i + 32i2)) = 0 Combine like terms: 16i + 24i = 40i (12 + 40i + 32i2) = 0 Solving 12 + 40i + 32i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + 10i + 8i2) = 0 Factor a trinomial. 4((3 + 4i)(1 + 2i)) = 0 Ignore the factor 4.Subproblem 1
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 = -0.75Subproblem 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 = {-0.75, -0.5}
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