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Simplifying 0 = 4i(-2 + -8i) 0 = (-2 * 4i + -8i * 4i) 0 = (-8i + -32i2) Solving 0 = -8i + -32i2 Solving for variable 'i'. Remove the zero: 8i + 32i2 = -8i + -32i2 + 8i + 32i2 Reorder the terms: 8i + 32i2 = -8i + 8i + -32i2 + 32i2 Combine like terms: -8i + 8i = 0 8i + 32i2 = 0 + -32i2 + 32i2 8i + 32i2 = -32i2 + 32i2 Combine like terms: -32i2 + 32i2 = 0 8i + 32i2 = 0 Factor out the Greatest Common Factor (GCF), '8i'. 8i(1 + 4i) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 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 = {0, -0.25}
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