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Simplifying -1i + -3(5 + -4i) + -1(2 + -3i) = 0 -1i + (5 * -3 + -4i * -3) + -1(2 + -3i) = 0 -1i + (-15 + 12i) + -1(2 + -3i) = 0 -1i + -15 + 12i + (2 * -1 + -3i * -1) = 0 -1i + -15 + 12i + (-2 + 3i) = 0 Reorder the terms: -15 + -2 + -1i + 12i + 3i = 0 Combine like terms: -15 + -2 = -17 -17 + -1i + 12i + 3i = 0 Combine like terms: -1i + 12i = 11i -17 + 11i + 3i = 0 Combine like terms: 11i + 3i = 14i -17 + 14i = 0 Solving -17 + 14i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 14i = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 14i = 0 + 17 14i = 0 + 17 Combine like terms: 0 + 17 = 17 14i = 17 Divide each side by '14'. i = 1.214285714 Simplifying i = 1.214285714
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