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Simplifying (4i)(5i)(-1 + 4i) = 0 Remove parenthesis around (4i) 4i(5i)(-1 + 4i) = 0 Remove parenthesis around (5i) 4i * 5i(-1 + 4i) = 0 Reorder the terms for easier multiplication: 4 * 5i * i(-1 + 4i) = 0 Multiply 4 * 5 20i * i(-1 + 4i) = 0 Multiply i * i 20i2(-1 + 4i) = 0 (-1 * 20i2 + 4i * 20i2) = 0 (-20i2 + 80i3) = 0 Solving -20i2 + 80i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '20i2'. 20i2(-1 + 4i) = 0 Ignore the factor 20.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 + 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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