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Simplifying (2 + -2i)(4 + -3i) = 0 Multiply (2 + -2i) * (4 + -3i) (2(4 + -3i) + -2i * (4 + -3i)) = 0 ((4 * 2 + -3i * 2) + -2i * (4 + -3i)) = 0 ((8 + -6i) + -2i * (4 + -3i)) = 0 (8 + -6i + (4 * -2i + -3i * -2i)) = 0 (8 + -6i + (-8i + 6i2)) = 0 Combine like terms: -6i + -8i = -14i (8 + -14i + 6i2) = 0 Solving 8 + -14i + 6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -7i + 3i2) = 0 Factor a trinomial. 2((1 + -1i)(4 + -3i)) = 0 Ignore the factor 2.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 + -3i)' equal to zero and attempt to solve: Simplifying 4 + -3i = 0 Solving 4 + -3i = 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 + -3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3i = 0 + -4 -3i = 0 + -4 Combine like terms: 0 + -4 = -4 -3i = -4 Divide each side by '-3'. i = 1.333333333 Simplifying i = 1.333333333Solution
i = {1, 1.333333333}
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