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Simplifying (10 + 5i) + -1(6 + -2i) + (3 + 4i) = 0 Remove parenthesis around (10 + 5i) 10 + 5i + -1(6 + -2i) + (3 + 4i) = 0 10 + 5i + (6 * -1 + -2i * -1) + (3 + 4i) = 0 10 + 5i + (-6 + 2i) + (3 + 4i) = 0 Remove parenthesis around (3 + 4i) 10 + 5i + -6 + 2i + 3 + 4i = 0 Reorder the terms: 10 + -6 + 3 + 5i + 2i + 4i = 0 Combine like terms: 10 + -6 = 4 4 + 3 + 5i + 2i + 4i = 0 Combine like terms: 4 + 3 = 7 7 + 5i + 2i + 4i = 0 Combine like terms: 5i + 2i = 7i 7 + 7i + 4i = 0 Combine like terms: 7i + 4i = 11i 7 + 11i = 0 Solving 7 + 11i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 11i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 11i = 0 + -7 11i = 0 + -7 Combine like terms: 0 + -7 = -7 11i = -7 Divide each side by '11'. i = -0.6363636364 Simplifying i = -0.6363636364
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