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Simplifying 4(3 + -1i) + 3(-5 + 2i) = 0 (3 * 4 + -1i * 4) + 3(-5 + 2i) = 0 (12 + -4i) + 3(-5 + 2i) = 0 12 + -4i + (-5 * 3 + 2i * 3) = 0 12 + -4i + (-15 + 6i) = 0 Reorder the terms: 12 + -15 + -4i + 6i = 0 Combine like terms: 12 + -15 = -3 -3 + -4i + 6i = 0 Combine like terms: -4i + 6i = 2i -3 + 2i = 0 Solving -3 + 2i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2i = 0 + 3 2i = 0 + 3 Combine like terms: 0 + 3 = 3 2i = 3 Divide each side by '2'. i = 1.5 Simplifying i = 1.5
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