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Simplifying (1 + 2i)(2 + 3i) = 0 Multiply (1 + 2i) * (2 + 3i) (1(2 + 3i) + 2i * (2 + 3i)) = 0 ((2 * 1 + 3i * 1) + 2i * (2 + 3i)) = 0 ((2 + 3i) + 2i * (2 + 3i)) = 0 (2 + 3i + (2 * 2i + 3i * 2i)) = 0 (2 + 3i + (4i + 6i2)) = 0 Combine like terms: 3i + 4i = 7i (2 + 7i + 6i2) = 0 Solving 2 + 7i + 6i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + 3i)(1 + 2i) = 0Subproblem 1
Set the factor '(2 + 3i)' equal to zero and attempt to solve: Simplifying 2 + 3i = 0 Solving 2 + 3i = 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 + 3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3i = 0 + -2 3i = 0 + -2 Combine like terms: 0 + -2 = -2 3i = -2 Divide each side by '3'. i = -0.6666666667 Simplifying i = -0.6666666667Subproblem 2
Set the factor '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Solution
i = {-0.6666666667, -0.5}
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