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Simplifying (7i)(-4i)(1 + 4i) = 0 Remove parenthesis around (7i) 7i(-4i)(1 + 4i) = 0 Remove parenthesis around (-4i) 7i * -4i(1 + 4i) = 0 Reorder the terms for easier multiplication: 7 * -4i * i(1 + 4i) = 0 Multiply 7 * -4 -28i * i(1 + 4i) = 0 Multiply i * i -28i2(1 + 4i) = 0 (1 * -28i2 + 4i * -28i2) = 0 (-28i2 + -112i3) = 0 Solving -28i2 + -112i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-28i2'. -28i2(1 + 4i) = 0 Ignore the factor -28.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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