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Simplifying (8 + i)(-1 + 4i) = 0 Multiply (8 + i) * (-1 + 4i) (8(-1 + 4i) + i(-1 + 4i)) = 0 ((-1 * 8 + 4i * 8) + i(-1 + 4i)) = 0 ((-8 + 32i) + i(-1 + 4i)) = 0 (-8 + 32i + (-1 * i + 4i * i)) = 0 (-8 + 32i + (-1i + 4i2)) = 0 Combine like terms: 32i + -1i = 31i (-8 + 31i + 4i2) = 0 Solving -8 + 31i + 4i2 = 0 Solving for variable 'i'. Factor a trinomial. (-8 + -1i)(1 + -4i) = 0Subproblem 1
Set the factor '(-8 + -1i)' equal to zero and attempt to solve: Simplifying -8 + -1i = 0 Solving -8 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1i = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1i = 0 + 8 -1i = 0 + 8 Combine like terms: 0 + 8 = 8 -1i = 8 Divide each side by '-1'. i = -8 Simplifying i = -8Subproblem 2
Set the factor '(1 + -4i)' equal to zero and attempt to solve: Simplifying 1 + -4i = 0 Solving 1 + -4i = 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 + -4i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4i = 0 + -1 -4i = 0 + -1 Combine like terms: 0 + -1 = -1 -4i = -1 Divide each side by '-4'. i = 0.25 Simplifying i = 0.25Solution
i = {-8, 0.25}
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