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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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