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Simplifying 0 = (5 + 3i) + -1(2 + 2i) Remove parenthesis around (5 + 3i) 0 = 5 + 3i + -1(2 + 2i) 0 = 5 + 3i + (2 * -1 + 2i * -1) 0 = 5 + 3i + (-2 + -2i) Reorder the terms: 0 = 5 + -2 + 3i + -2i Combine like terms: 5 + -2 = 3 0 = 3 + 3i + -2i Combine like terms: 3i + -2i = 1i 0 = 3 + 1i Solving 0 = 3 + 1i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1i' to each side of the equation. 0 + -1i = 3 + 1i + -1i Remove the zero: -1i = 3 + 1i + -1i Combine like terms: 1i + -1i = 0 -1i = 3 + 0 -1i = 3 Divide each side by '-1'. i = -3 Simplifying i = -3
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