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Simplifying (7 + -1i) + -1(-3 + 3i) = 0 Remove parenthesis around (7 + -1i) 7 + -1i + -1(-3 + 3i) = 0 7 + -1i + (-3 * -1 + 3i * -1) = 0 7 + -1i + (3 + -3i) = 0 Reorder the terms: 7 + 3 + -1i + -3i = 0 Combine like terms: 7 + 3 = 10 10 + -1i + -3i = 0 Combine like terms: -1i + -3i = -4i 10 + -4i = 0 Solving 10 + -4i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -4i = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -4i = 0 + -10 -4i = 0 + -10 Combine like terms: 0 + -10 = -10 -4i = -10 Divide each side by '-4'. i = 2.5 Simplifying i = 2.5
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