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Simplifying (8 + 5i)(6 + 3i) = 0 Multiply (8 + 5i) * (6 + 3i) (8(6 + 3i) + 5i * (6 + 3i)) = 0 ((6 * 8 + 3i * 8) + 5i * (6 + 3i)) = 0 ((48 + 24i) + 5i * (6 + 3i)) = 0 (48 + 24i + (6 * 5i + 3i * 5i)) = 0 (48 + 24i + (30i + 15i2)) = 0 Combine like terms: 24i + 30i = 54i (48 + 54i + 15i2) = 0 Solving 48 + 54i + 15i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(16 + 18i + 5i2) = 0 Factor a trinomial. 3((2 + i)(8 + 5i)) = 0 Ignore the factor 3.Subproblem 1
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 = -2Subproblem 2
Set the factor '(8 + 5i)' equal to zero and attempt to solve: Simplifying 8 + 5i = 0 Solving 8 + 5i = 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 + 5i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5i = 0 + -8 5i = 0 + -8 Combine like terms: 0 + -8 = -8 5i = -8 Divide each side by '5'. i = -1.6 Simplifying i = -1.6Solution
i = {-2, -1.6}
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