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Simplifying (6 + -3i)(10 + 2i) = 0 Multiply (6 + -3i) * (10 + 2i) (6(10 + 2i) + -3i * (10 + 2i)) = 0 ((10 * 6 + 2i * 6) + -3i * (10 + 2i)) = 0 ((60 + 12i) + -3i * (10 + 2i)) = 0 (60 + 12i + (10 * -3i + 2i * -3i)) = 0 (60 + 12i + (-30i + -6i2)) = 0 Combine like terms: 12i + -30i = -18i (60 + -18i + -6i2) = 0 Solving 60 + -18i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '6'. 6(10 + -3i + -1i2) = 0 Factor a trinomial. 6((2 + -1i)(5 + i)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Subproblem 2
Set the factor '(5 + i)' equal to zero and attempt to solve: Simplifying 5 + i = 0 Solving 5 + i = 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 + i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + i = 0 + -5 i = 0 + -5 Combine like terms: 0 + -5 = -5 i = -5 Simplifying i = -5Solution
i = {2, -5}
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