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Simplifying (4 + -1i)(6 + -6i) = 0 Multiply (4 + -1i) * (6 + -6i) (4(6 + -6i) + -1i * (6 + -6i)) = 0 ((6 * 4 + -6i * 4) + -1i * (6 + -6i)) = 0 ((24 + -24i) + -1i * (6 + -6i)) = 0 (24 + -24i + (6 * -1i + -6i * -1i)) = 0 (24 + -24i + (-6i + 6i2)) = 0 Combine like terms: -24i + -6i = -30i (24 + -30i + 6i2) = 0 Solving 24 + -30i + 6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '6'. 6(4 + -5i + i2) = 0 Factor a trinomial. 6((1 + -1i)(4 + -1i)) = 0 Ignore the factor 6.Subproblem 1
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 = 1Subproblem 2
Set the factor '(4 + -1i)' equal to zero and attempt to solve: Simplifying 4 + -1i = 0 Solving 4 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i = 0 + -4 -1i = 0 + -4 Combine like terms: 0 + -4 = -4 -1i = -4 Divide each side by '-1'. i = 4 Simplifying i = 4Solution
i = {1, 4}
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