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Simplifying (-4 + 11i)(-5 + -8i) = 0 Multiply (-4 + 11i) * (-5 + -8i) (-4(-5 + -8i) + 11i * (-5 + -8i)) = 0 ((-5 * -4 + -8i * -4) + 11i * (-5 + -8i)) = 0 ((20 + 32i) + 11i * (-5 + -8i)) = 0 (20 + 32i + (-5 * 11i + -8i * 11i)) = 0 (20 + 32i + (-55i + -88i2)) = 0 Combine like terms: 32i + -55i = -23i (20 + -23i + -88i2) = 0 Solving 20 + -23i + -88i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -11i)(5 + 8i) = 0Subproblem 1
Set the factor '(4 + -11i)' equal to zero and attempt to solve: Simplifying 4 + -11i = 0 Solving 4 + -11i = 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 + -11i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -11i = 0 + -4 -11i = 0 + -4 Combine like terms: 0 + -4 = -4 -11i = -4 Divide each side by '-11'. i = 0.3636363636 Simplifying i = 0.3636363636Subproblem 2
Set the factor '(5 + 8i)' equal to zero and attempt to solve: Simplifying 5 + 8i = 0 Solving 5 + 8i = 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 + 8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8i = 0 + -5 8i = 0 + -5 Combine like terms: 0 + -5 = -5 8i = -5 Divide each side by '8'. i = -0.625 Simplifying i = -0.625Solution
i = {0.3636363636, -0.625}
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