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Simplifying 2(5 + -1i) + -5(3 + -3i) = 0 (5 * 2 + -1i * 2) + -5(3 + -3i) = 0 (10 + -2i) + -5(3 + -3i) = 0 10 + -2i + (3 * -5 + -3i * -5) = 0 10 + -2i + (-15 + 15i) = 0 Reorder the terms: 10 + -15 + -2i + 15i = 0 Combine like terms: 10 + -15 = -5 -5 + -2i + 15i = 0 Combine like terms: -2i + 15i = 13i -5 + 13i = 0 Solving -5 + 13i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 13i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 13i = 0 + 5 13i = 0 + 5 Combine like terms: 0 + 5 = 5 13i = 5 Divide each side by '13'. i = 0.3846153846 Simplifying i = 0.3846153846
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