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Simplifying i + (3 + -5i) + -2(2 + -3i) = 0 Remove parenthesis around (3 + -5i) i + 3 + -5i + -2(2 + -3i) = 0 i + 3 + -5i + (2 * -2 + -3i * -2) = 0 i + 3 + -5i + (-4 + 6i) = 0 Reorder the terms: 3 + -4 + i + -5i + 6i = 0 Combine like terms: 3 + -4 = -1 -1 + i + -5i + 6i = 0 Combine like terms: i + -5i = -4i -1 + -4i + 6i = 0 Combine like terms: -4i + 6i = 2i -1 + 2i = 0 Solving -1 + 2i = 0 Solving for variable 'i'. 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 = 0.5
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