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Simplifying (2i)(1 + -4i)(1 + i) = 0 Remove parenthesis around (2i) 2i(1 + -4i)(1 + i) = 0 Multiply (1 + -4i) * (1 + i) 2i(1(1 + i) + -4i * (1 + i)) = 0 2i((1 * 1 + i * 1) + -4i * (1 + i)) = 0 2i((1 + 1i) + -4i * (1 + i)) = 0 2i(1 + 1i + (1 * -4i + i * -4i)) = 0 2i(1 + 1i + (-4i + -4i2)) = 0 Combine like terms: 1i + -4i = -3i 2i(1 + -3i + -4i2) = 0 (1 * 2i + -3i * 2i + -4i2 * 2i) = 0 (2i + -6i2 + -8i3) = 0 Solving 2i + -6i2 + -8i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2i'. 2i(1 + -3i + -4i2) = 0 Factor a trinomial. 2i((1 + -4i)(1 + i)) = 0 Ignore the factor 2.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 = 0.25Subproblem 3
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 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 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {0, 0.25, -1}
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