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Simplifying (3 + 4i) + -1(-5 + -1i) = 0 Remove parenthesis around (3 + 4i) 3 + 4i + -1(-5 + -1i) = 0 3 + 4i + (-5 * -1 + -1i * -1) = 0 3 + 4i + (5 + 1i) = 0 Reorder the terms: 3 + 5 + 4i + 1i = 0 Combine like terms: 3 + 5 = 8 8 + 4i + 1i = 0 Combine like terms: 4i + 1i = 5i 8 + 5i = 0 Solving 8 + 5i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5i = 0 + -8 5i = 0 + -8 Combine like terms: 0 + -8 = -8 5i = -8 Divide each side by '5'. i = -1.6 Simplifying i = -1.6
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