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Simplifying 0 = (-4 + 11i)(-5 + -8i) Multiply (-4 + 11i) * (-5 + -8i) 0 = (-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)) Combine like terms: 32i + -55i = -23i 0 = (20 + -23i + -88i2) Solving 0 = 20 + -23i + -88i2 Solving for variable 'i'. Combine like terms: 0 + -20 = -20 -20 + 23i + 88i2 = 20 + -23i + -88i2 + -20 + 23i + 88i2 Reorder the terms: -20 + 23i + 88i2 = 20 + -20 + -23i + 23i + -88i2 + 88i2 Combine like terms: 20 + -20 = 0 -20 + 23i + 88i2 = 0 + -23i + 23i + -88i2 + 88i2 -20 + 23i + 88i2 = -23i + 23i + -88i2 + 88i2 Combine like terms: -23i + 23i = 0 -20 + 23i + 88i2 = 0 + -88i2 + 88i2 -20 + 23i + 88i2 = -88i2 + 88i2 Combine like terms: -88i2 + 88i2 = 0 -20 + 23i + 88i2 = 0 Factor a trinomial. (-5 + -8i)(4 + -11i) = 0Subproblem 1
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 = -0.625Subproblem 2
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 = 0.3636363636Solution
i = {-0.625, 0.3636363636}
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