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Simplifying 5i + -3(2i + -1) = 3i + 8 Reorder the terms: 5i + -3(-1 + 2i) = 3i + 8 5i + (-1 * -3 + 2i * -3) = 3i + 8 5i + (3 + -6i) = 3i + 8 Reorder the terms: 3 + 5i + -6i = 3i + 8 Combine like terms: 5i + -6i = -1i 3 + -1i = 3i + 8 Reorder the terms: 3 + -1i = 8 + 3i Solving 3 + -1i = 8 + 3i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3i' to each side of the equation. 3 + -1i + -3i = 8 + 3i + -3i Combine like terms: -1i + -3i = -4i 3 + -4i = 8 + 3i + -3i Combine like terms: 3i + -3i = 0 3 + -4i = 8 + 0 3 + -4i = 8 Add '-3' to each side of the equation. 3 + -3 + -4i = 8 + -3 Combine like terms: 3 + -3 = 0 0 + -4i = 8 + -3 -4i = 8 + -3 Combine like terms: 8 + -3 = 5 -4i = 5 Divide each side by '-4'. i = -1.25 Simplifying i = -1.25
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