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Simplifying (-8i)(-1i)(-1 + 2i) = 0 Remove parenthesis around (-8i) -8i(-1i)(-1 + 2i) = 0 Remove parenthesis around (-1i) -8i * -1i(-1 + 2i) = 0 Reorder the terms for easier multiplication: -8 * -1i * i(-1 + 2i) = 0 Multiply -8 * -1 8i * i(-1 + 2i) = 0 Multiply i * i 8i2(-1 + 2i) = 0 (-1 * 8i2 + 2i * 8i2) = 0 (-8i2 + 16i3) = 0 Solving -8i2 + 16i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '8i2'. 8i2(-1 + 2i) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'i2' equal to zero and attempt to solve: Simplifying i2 = 0 Solving i2 = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i2 = 0 Take the square root of each side: i = {0}Subproblem 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, 0.5}
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