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Simplifying (1 + -4i) + -1(3 * 5i) + -1(-4 + i) = 0 Remove parenthesis around (1 + -4i) 1 + -4i + -1(3 * 5i) + -1(-4 + i) = 0 Multiply 3 * 5 1 + -4i + -1(15i) + -1(-4 + i) = 0 Remove parenthesis around (15i) 1 + -4i + -1 * 15i + -1(-4 + i) = 0 Multiply -1 * 15 1 + -4i + -15i + -1(-4 + i) = 0 1 + -4i + -15i + (-4 * -1 + i * -1) = 0 1 + -4i + -15i + (4 + -1i) = 0 Reorder the terms: 1 + 4 + -4i + -15i + -1i = 0 Combine like terms: 1 + 4 = 5 5 + -4i + -15i + -1i = 0 Combine like terms: -4i + -15i = -19i 5 + -19i + -1i = 0 Combine like terms: -19i + -1i = -20i 5 + -20i = 0 Solving 5 + -20i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -20i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -20i = 0 + -5 -20i = 0 + -5 Combine like terms: 0 + -5 = -5 -20i = -5 Divide each side by '-20'. i = 0.25 Simplifying i = 0.25
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