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Simplifying 4(3 + 3i) + -1(4 + i) = 0 (3 * 4 + 3i * 4) + -1(4 + i) = 0 (12 + 12i) + -1(4 + i) = 0 12 + 12i + (4 * -1 + i * -1) = 0 12 + 12i + (-4 + -1i) = 0 Reorder the terms: 12 + -4 + 12i + -1i = 0 Combine like terms: 12 + -4 = 8 8 + 12i + -1i = 0 Combine like terms: 12i + -1i = 11i 8 + 11i = 0 Solving 8 + 11i = 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 + 11i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 11i = 0 + -8 11i = 0 + -8 Combine like terms: 0 + -8 = -8 11i = -8 Divide each side by '11'. i = -0.7272727273 Simplifying i = -0.7272727273
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