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Simplifying (1 + 2i) + -1(3 + 4i) = 0 Remove parenthesis around (1 + 2i) 1 + 2i + -1(3 + 4i) = 0 1 + 2i + (3 * -1 + 4i * -1) = 0 1 + 2i + (-3 + -4i) = 0 Reorder the terms: 1 + -3 + 2i + -4i = 0 Combine like terms: 1 + -3 = -2 -2 + 2i + -4i = 0 Combine like terms: 2i + -4i = -2i -2 + -2i = 0 Solving -2 + -2i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -2i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2i = 0 + 2 -2i = 0 + 2 Combine like terms: 0 + 2 = 2 -2i = 2 Divide each side by '-2'. i = -1 Simplifying i = -1
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