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Simplifying 2z + -1(4 + i) = 8 + i 2z + (4 * -1 + i * -1) = 8 + i 2z + (-4 + -1i) = 8 + i Reorder the terms: -4 + -1i + 2z = 8 + i Solving -4 + -1i + 2z = 8 + i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1i' to each side of the equation. -4 + -1i + -1i + 2z = 8 + i + -1i Combine like terms: -1i + -1i = -2i -4 + -2i + 2z = 8 + i + -1i Combine like terms: i + -1i = 0 -4 + -2i + 2z = 8 + 0 -4 + -2i + 2z = 8 Add '4' to each side of the equation. -4 + -2i + 4 + 2z = 8 + 4 Reorder the terms: -4 + 4 + -2i + 2z = 8 + 4 Combine like terms: -4 + 4 = 0 0 + -2i + 2z = 8 + 4 -2i + 2z = 8 + 4 Combine like terms: 8 + 4 = 12 -2i + 2z = 12 Add '-2z' to each side of the equation. -2i + 2z + -2z = 12 + -2z Combine like terms: 2z + -2z = 0 -2i + 0 = 12 + -2z -2i = 12 + -2z Divide each side by '-2'. i = -6 + z Simplifying i = -6 + z
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