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Simplifying (5i)(-7i)(2 + 8i) = 0 Remove parenthesis around (5i) 5i(-7i)(2 + 8i) = 0 Remove parenthesis around (-7i) 5i * -7i(2 + 8i) = 0 Reorder the terms for easier multiplication: 5 * -7i * i(2 + 8i) = 0 Multiply 5 * -7 -35i * i(2 + 8i) = 0 Multiply i * i -35i2(2 + 8i) = 0 (2 * -35i2 + 8i * -35i2) = 0 (-70i2 + -280i3) = 0 Solving -70i2 + -280i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-70i2'. -70i2(1 + 4i) = 0 Ignore the factor -70.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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