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Simplifying (-9 + 9i)(3 + i) = 0 Multiply (-9 + 9i) * (3 + i) (-9(3 + i) + 9i * (3 + i)) = 0 ((3 * -9 + i * -9) + 9i * (3 + i)) = 0 ((-27 + -9i) + 9i * (3 + i)) = 0 (-27 + -9i + (3 * 9i + i * 9i)) = 0 (-27 + -9i + (27i + 9i2)) = 0 Combine like terms: -9i + 27i = 18i (-27 + 18i + 9i2) = 0 Solving -27 + 18i + 9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '9'. 9(-3 + 2i + i2) = 0 Factor a trinomial. 9((-3 + -1i)(1 + -1i)) = 0 Ignore the factor 9.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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