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Simplifying (8 + -7i)(6 + 3i) = 0 Multiply (8 + -7i) * (6 + 3i) (8(6 + 3i) + -7i * (6 + 3i)) = 0 ((6 * 8 + 3i * 8) + -7i * (6 + 3i)) = 0 ((48 + 24i) + -7i * (6 + 3i)) = 0 (48 + 24i + (6 * -7i + 3i * -7i)) = 0 (48 + 24i + (-42i + -21i2)) = 0 Combine like terms: 24i + -42i = -18i (48 + -18i + -21i2) = 0 Solving 48 + -18i + -21i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(16 + -6i + -7i2) = 0 Factor a trinomial. 3((8 + -7i)(2 + i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -7i)' equal to zero and attempt to solve: Simplifying 8 + -7i = 0 Solving 8 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7i = 0 + -8 -7i = 0 + -8 Combine like terms: 0 + -8 = -8 -7i = -8 Divide each side by '-7'. i = 1.142857143 Simplifying i = 1.142857143Subproblem 2
Set the factor '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Solution
i = {1.142857143, -2}
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