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Simplifying (4 + 6i) + -1(3 + 2i) = (1 + -4) Remove parenthesis around (4 + 6i) 4 + 6i + -1(3 + 2i) = (1 + -4) 4 + 6i + (3 * -1 + 2i * -1) = (1 + -4) 4 + 6i + (-3 + -2i) = (1 + -4) Reorder the terms: 4 + -3 + 6i + -2i = (1 + -4) Combine like terms: 4 + -3 = 1 1 + 6i + -2i = (1 + -4) Combine like terms: 6i + -2i = 4i 1 + 4i = (1 + -4) Combine like terms: 1 + -4 = -3 1 + 4i = (-3) 1 + 4i = -3 Solving 1 + 4i = -3 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 + 4i = -3 + -1 Combine like terms: 1 + -1 = 0 0 + 4i = -3 + -1 4i = -3 + -1 Combine like terms: -3 + -1 = -4 4i = -4 Divide each side by '4'. i = -1 Simplifying i = -1
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