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Simplifying (i)(-7i)(5 + 8i) = 0 Remove parenthesis around (-7i) i * -7i(5 + 8i) = 0 Reorder the terms for easier multiplication: -7i * i(5 + 8i) = 0 Multiply i * i -7i2(5 + 8i) = 0 (5 * -7i2 + 8i * -7i2) = 0 (-35i2 + -56i3) = 0 Solving -35i2 + -56i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-7i2'. -7i2(5 + 8i) = 0 Ignore the factor -7.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 '(5 + 8i)' equal to zero and attempt to solve: Simplifying 5 + 8i = 0 Solving 5 + 8i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8i = 0 + -5 8i = 0 + -5 Combine like terms: 0 + -5 = -5 8i = -5 Divide each side by '8'. i = -0.625 Simplifying i = -0.625Solution
i = {0, -0.625}
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