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Simplifying (5 + 7i)(4 + -12i) = 0 Multiply (5 + 7i) * (4 + -12i) (5(4 + -12i) + 7i * (4 + -12i)) = 0 ((4 * 5 + -12i * 5) + 7i * (4 + -12i)) = 0 ((20 + -60i) + 7i * (4 + -12i)) = 0 (20 + -60i + (4 * 7i + -12i * 7i)) = 0 (20 + -60i + (28i + -84i2)) = 0 Combine like terms: -60i + 28i = -32i (20 + -32i + -84i2) = 0 Solving 20 + -32i + -84i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -8i + -21i2) = 0 Factor a trinomial. 4((1 + -3i)(5 + 7i)) = 0 Ignore the factor 4.Subproblem 1
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 = 0.3333333333Subproblem 2
Set the factor '(5 + 7i)' equal to zero and attempt to solve: Simplifying 5 + 7i = 0 Solving 5 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 7i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7i = 0 + -5 7i = 0 + -5 Combine like terms: 0 + -5 = -5 7i = -5 Divide each side by '7'. i = -0.7142857143 Simplifying i = -0.7142857143Solution
i = {0.3333333333, -0.7142857143}
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