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Simplifying (7 + -1i) + -1(8 + 3i) = 0 Remove parenthesis around (7 + -1i) 7 + -1i + -1(8 + 3i) = 0 7 + -1i + (8 * -1 + 3i * -1) = 0 7 + -1i + (-8 + -3i) = 0 Reorder the terms: 7 + -8 + -1i + -3i = 0 Combine like terms: 7 + -8 = -1 -1 + -1i + -3i = 0 Combine like terms: -1i + -3i = -4i -1 + -4i = 0 Solving -1 + -4i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4i = 0 + 1 -4i = 0 + 1 Combine like terms: 0 + 1 = 1 -4i = 1 Divide each side by '-4'. i = -0.25 Simplifying i = -0.25
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