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Simplifying (8 + -2i)(6 + 3i) = 0 Multiply (8 + -2i) * (6 + 3i) (8(6 + 3i) + -2i * (6 + 3i)) = 0 ((6 * 8 + 3i * 8) + -2i * (6 + 3i)) = 0 ((48 + 24i) + -2i * (6 + 3i)) = 0 (48 + 24i + (6 * -2i + 3i * -2i)) = 0 (48 + 24i + (-12i + -6i2)) = 0 Combine like terms: 24i + -12i = 12i (48 + 12i + -6i2) = 0 Solving 48 + 12i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '6'. 6(8 + 2i + -1i2) = 0 Factor a trinomial. 6((4 + -1i)(2 + i)) = 0 Ignore the factor 6.Subproblem 1
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 = 4Subproblem 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 = {4, -2}
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