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Simplifying 7 + -1(-2 + 3i) + -1(-3 + -1i) = 0 7 + (-2 * -1 + 3i * -1) + -1(-3 + -1i) = 0 7 + (2 + -3i) + -1(-3 + -1i) = 0 7 + 2 + -3i + (-3 * -1 + -1i * -1) = 0 7 + 2 + -3i + (3 + 1i) = 0 Reorder the terms: 7 + 2 + 3 + -3i + 1i = 0 Combine like terms: 7 + 2 = 9 9 + 3 + -3i + 1i = 0 Combine like terms: 9 + 3 = 12 12 + -3i + 1i = 0 Combine like terms: -3i + 1i = -2i 12 + -2i = 0 Solving 12 + -2i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -2i = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -2i = 0 + -12 -2i = 0 + -12 Combine like terms: 0 + -12 = -12 -2i = -12 Divide each side by '-2'. i = 6 Simplifying i = 6
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