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Simplifying (7i)(3i)(-8 + -6i) = 0 Remove parenthesis around (7i) 7i(3i)(-8 + -6i) = 0 Remove parenthesis around (3i) 7i * 3i(-8 + -6i) = 0 Reorder the terms for easier multiplication: 7 * 3i * i(-8 + -6i) = 0 Multiply 7 * 3 21i * i(-8 + -6i) = 0 Multiply i * i 21i2(-8 + -6i) = 0 (-8 * 21i2 + -6i * 21i2) = 0 (-168i2 + -126i3) = 0 Solving -168i2 + -126i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-42i2'. -42i2(4 + 3i) = 0 Ignore the factor -42.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 '(4 + 3i)' equal to zero and attempt to solve: Simplifying 4 + 3i = 0 Solving 4 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3i = 0 + -4 3i = 0 + -4 Combine like terms: 0 + -4 = -4 3i = -4 Divide each side by '3'. i = -1.333333333 Simplifying i = -1.333333333Solution
i = {0, -1.333333333}
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