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Simplifying (i)(8i)(-4 + 7i) = 0 Remove parenthesis around (8i) i * 8i(-4 + 7i) = 0 Reorder the terms for easier multiplication: 8i * i(-4 + 7i) = 0 Multiply i * i 8i2(-4 + 7i) = 0 (-4 * 8i2 + 7i * 8i2) = 0 (-32i2 + 56i3) = 0 Solving -32i2 + 56i3 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '8i2'. 8i2(-4 + 7i) = 0 Ignore the factor 8.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 + 7i)' equal to zero and attempt to solve: Simplifying -4 + 7i = 0 Solving -4 + 7i = 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 + 7i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7i = 0 + 4 7i = 0 + 4 Combine like terms: 0 + 4 = 4 7i = 4 Divide each side by '7'. i = 0.5714285714 Simplifying i = 0.5714285714Solution
i = {0, 0.5714285714}
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