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Simplifying (2 + i)(-3 + 9i) = 0 Multiply (2 + i) * (-3 + 9i) (2(-3 + 9i) + i(-3 + 9i)) = 0 ((-3 * 2 + 9i * 2) + i(-3 + 9i)) = 0 ((-6 + 18i) + i(-3 + 9i)) = 0 (-6 + 18i + (-3 * i + 9i * i)) = 0 (-6 + 18i + (-3i + 9i2)) = 0 Combine like terms: 18i + -3i = 15i (-6 + 15i + 9i2) = 0 Solving -6 + 15i + 9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 5i + 3i2) = 0 Factor a trinomial. 3((-2 + -1i)(1 + -3i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1i)' equal to zero and attempt to solve: Simplifying -2 + -1i = 0 Solving -2 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1i = 0 + 2 -1i = 0 + 2 Combine like terms: 0 + 2 = 2 -1i = 2 Divide each side by '-1'. i = -2 Simplifying i = -2Subproblem 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 = {-2, 0.3333333333}
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