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