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Simplifying 2i(4i + -7i) + -3i(2 + 4i) = 0 Combine like terms: 4i + -7i = -3i 2i(-3i) + -3i(2 + 4i) = 0 Remove parenthesis around (-3i) 2i * -3i + -3i(2 + 4i) = 0 Reorder the terms for easier multiplication: 2 * -3i * i + -3i(2 + 4i) = 0 Multiply 2 * -3 -6i * i + -3i(2 + 4i) = 0 Multiply i * i -6i2 + -3i(2 + 4i) = 0 -6i2 + (2 * -3i + 4i * -3i) = 0 -6i2 + (-6i + -12i2) = 0 Reorder the terms: -6i + -6i2 + -12i2 = 0 Combine like terms: -6i2 + -12i2 = -18i2 -6i + -18i2 = 0 Solving -6i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-6i'. -6i(1 + 3i) = 0 Ignore the factor -6.Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
Set the factor '(1 + 3i)' equal to zero and attempt to solve: Simplifying 1 + 3i = 0 Solving 1 + 3i = 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 + 3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3i = 0 + -1 3i = 0 + -1 Combine like terms: 0 + -1 = -1 3i = -1 Divide each side by '3'. i = -0.3333333333 Simplifying i = -0.3333333333Solution
i = {0, -0.3333333333}
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