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Simplifying (8 + 3i) + -1(5.3 + i) + (8.6 + -5i) = 0 Remove parenthesis around (8 + 3i) 8 + 3i + -1(5.3 + i) + (8.6 + -5i) = 0 8 + 3i + (5.3 * -1 + i * -1) + (8.6 + -5i) = 0 8 + 3i + (-5.3 + -1i) + (8.6 + -5i) = 0 Remove parenthesis around (8.6 + -5i) 8 + 3i + -5.3 + -1i + 8.6 + -5i = 0 Reorder the terms: 8 + -5.3 + 8.6 + 3i + -1i + -5i = 0 Combine like terms: 8 + -5.3 = 2.7 2.7 + 8.6 + 3i + -1i + -5i = 0 Combine like terms: 2.7 + 8.6 = 11.3 11.3 + 3i + -1i + -5i = 0 Combine like terms: 3i + -1i = 2i 11.3 + 2i + -5i = 0 Combine like terms: 2i + -5i = -3i 11.3 + -3i = 0 Solving 11.3 + -3i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-11.3' to each side of the equation. 11.3 + -11.3 + -3i = 0 + -11.3 Combine like terms: 11.3 + -11.3 = 0.0 0.0 + -3i = 0 + -11.3 -3i = 0 + -11.3 Combine like terms: 0 + -11.3 = -11.3 -3i = -11.3 Divide each side by '-3'. i = 3.766666667 Simplifying i = 3.766666667
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