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Simplifying (-3 + -1i)(2 + -2i) = 0 Multiply (-3 + -1i) * (2 + -2i) (-3(2 + -2i) + -1i * (2 + -2i)) = 0 ((2 * -3 + -2i * -3) + -1i * (2 + -2i)) = 0 ((-6 + 6i) + -1i * (2 + -2i)) = 0 (-6 + 6i + (2 * -1i + -2i * -1i)) = 0 (-6 + 6i + (-2i + 2i2)) = 0 Combine like terms: 6i + -2i = 4i (-6 + 4i + 2i2) = 0 Solving -6 + 4i + 2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 2i + i2) = 0 Factor a trinomial. 2((-3 + -1i)(1 + -1i)) = 0 Ignore the factor 2.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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