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Simplifying -1i + -3 + -1(4 + -5i) + -1(5 + -3i) = 0 -1i + -3 + (4 * -1 + -5i * -1) + -1(5 + -3i) = 0 -1i + -3 + (-4 + 5i) + -1(5 + -3i) = 0 -1i + -3 + -4 + 5i + (5 * -1 + -3i * -1) = 0 -1i + -3 + -4 + 5i + (-5 + 3i) = 0 Reorder the terms: -3 + -4 + -5 + -1i + 5i + 3i = 0 Combine like terms: -3 + -4 = -7 -7 + -5 + -1i + 5i + 3i = 0 Combine like terms: -7 + -5 = -12 -12 + -1i + 5i + 3i = 0 Combine like terms: -1i + 5i = 4i -12 + 4i + 3i = 0 Combine like terms: 4i + 3i = 7i -12 + 7i = 0 Solving -12 + 7i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + 7i = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 7i = 0 + 12 7i = 0 + 12 Combine like terms: 0 + 12 = 12 7i = 12 Divide each side by '7'. i = 1.714285714 Simplifying i = 1.714285714
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