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Simplifying (x + -1(-1 + -2i)) = (x + -1(-1 + 2i)) (x + (-1 * -1 + -2i * -1)) = (x + -1(-1 + 2i)) (x + (1 + 2i)) = (x + -1(-1 + 2i)) Reorder the terms: (1 + 2i + x) = (x + -1(-1 + 2i)) Remove parenthesis around (1 + 2i + x) 1 + 2i + x = (x + -1(-1 + 2i)) 1 + 2i + x = (x + (-1 * -1 + 2i * -1)) 1 + 2i + x = (x + (1 + -2i)) Reorder the terms: 1 + 2i + x = (1 + -2i + x) Remove parenthesis around (1 + -2i + x) 1 + 2i + x = 1 + -2i + x Add '-1' to each side of the equation. 1 + 2i + -1 + x = 1 + -2i + -1 + x Reorder the terms: 1 + -1 + 2i + x = 1 + -2i + -1 + x Combine like terms: 1 + -1 = 0 0 + 2i + x = 1 + -2i + -1 + x 2i + x = 1 + -2i + -1 + x Reorder the terms: 2i + x = 1 + -1 + -2i + x Combine like terms: 1 + -1 = 0 2i + x = 0 + -2i + x 2i + x = -2i + x Add '-1x' to each side of the equation. 2i + x + -1x = -2i + x + -1x Combine like terms: x + -1x = 0 2i + 0 = -2i + x + -1x 2i = -2i + x + -1x Combine like terms: x + -1x = 0 2i = -2i + 0 2i = -2i Solving 2i = -2i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2i' to each side of the equation. 2i + 2i = -2i + 2i Combine like terms: 2i + 2i = 4i 4i = -2i + 2i Combine like terms: -2i + 2i = 0 4i = 0 Divide each side by '4'. i = 0 Simplifying i = 0
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