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Simplifying (4 + -1i) + -1(7 + 3i) = 0 Remove parenthesis around (4 + -1i) 4 + -1i + -1(7 + 3i) = 0 4 + -1i + (7 * -1 + 3i * -1) = 0 4 + -1i + (-7 + -3i) = 0 Reorder the terms: 4 + -7 + -1i + -3i = 0 Combine like terms: 4 + -7 = -3 -3 + -1i + -3i = 0 Combine like terms: -1i + -3i = -4i -3 + -4i = 0 Solving -3 + -4i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4i = 0 + 3 -4i = 0 + 3 Combine like terms: 0 + 3 = 3 -4i = 3 Divide each side by '-4'. i = -0.75 Simplifying i = -0.75
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