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Simplifying (8 + -3i)(3 + 2i) = 0 Multiply (8 + -3i) * (3 + 2i) (8(3 + 2i) + -3i * (3 + 2i)) = 0 ((3 * 8 + 2i * 8) + -3i * (3 + 2i)) = 0 ((24 + 16i) + -3i * (3 + 2i)) = 0 (24 + 16i + (3 * -3i + 2i * -3i)) = 0 (24 + 16i + (-9i + -6i2)) = 0 Combine like terms: 16i + -9i = 7i (24 + 7i + -6i2) = 0 Solving 24 + 7i + -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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