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Simplifying 3i2 + -2i = 9 + -8i Reorder the terms: -2i + 3i2 = 9 + -8i Solving -2i + 3i2 = 9 + -8i Solving for variable 'i'. Reorder the terms: -9 + -2i + 8i + 3i2 = 9 + -8i + -9 + 8i Combine like terms: -2i + 8i = 6i -9 + 6i + 3i2 = 9 + -8i + -9 + 8i Reorder the terms: -9 + 6i + 3i2 = 9 + -9 + -8i + 8i Combine like terms: 9 + -9 = 0 -9 + 6i + 3i2 = 0 + -8i + 8i -9 + 6i + 3i2 = -8i + 8i Combine like terms: -8i + 8i = 0 -9 + 6i + 3i2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 2i + i2) = 0 Factor a trinomial. 3((-3 + -1i)(1 + -1i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1i)' equal to zero and attempt to solve: Simplifying -3 + -1i = 0 Solving -3 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1i = 0 + 3 -1i = 0 + 3 Combine like terms: 0 + 3 = 3 -1i = 3 Divide each side by '-1'. i = -3 Simplifying i = -3Subproblem 2
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 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 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Solution
i = {-3, 1}
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