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Simplifying 5 + -1(-4 + 4i) + -1(-3 + -1i) = 0 5 + (-4 * -1 + 4i * -1) + -1(-3 + -1i) = 0 5 + (4 + -4i) + -1(-3 + -1i) = 0 5 + 4 + -4i + (-3 * -1 + -1i * -1) = 0 5 + 4 + -4i + (3 + 1i) = 0 Reorder the terms: 5 + 4 + 3 + -4i + 1i = 0 Combine like terms: 5 + 4 = 9 9 + 3 + -4i + 1i = 0 Combine like terms: 9 + 3 = 12 12 + -4i + 1i = 0 Combine like terms: -4i + 1i = -3i 12 + -3i = 0 Solving 12 + -3i = 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 + -3i = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -3i = 0 + -12 -3i = 0 + -12 Combine like terms: 0 + -12 = -12 -3i = -12 Divide each side by '-3'. i = 4 Simplifying i = 4
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