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Simplifying (3 + 2i)(8 + 3i) = 0 Multiply (3 + 2i) * (8 + 3i) (3(8 + 3i) + 2i * (8 + 3i)) = 0 ((8 * 3 + 3i * 3) + 2i * (8 + 3i)) = 0 ((24 + 9i) + 2i * (8 + 3i)) = 0 (24 + 9i + (8 * 2i + 3i * 2i)) = 0 (24 + 9i + (16i + 6i2)) = 0 Combine like terms: 9i + 16i = 25i (24 + 25i + 6i2) = 0 Solving 24 + 25i + 6i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + 3i)(3 + 2i) = 0Subproblem 1
Set the factor '(8 + 3i)' equal to zero and attempt to solve: Simplifying 8 + 3i = 0 Solving 8 + 3i = 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 + 3i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3i = 0 + -8 3i = 0 + -8 Combine like terms: 0 + -8 = -8 3i = -8 Divide each side by '3'. i = -2.666666667 Simplifying i = -2.666666667Subproblem 2
Set the factor '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Solution
i = {-2.666666667, -1.5}
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