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Simplifying z + (5 + -1i) = (0 + 1i) Remove parenthesis around (5 + -1i) z + 5 + -1i = (0 + 1i) Reorder the terms: 5 + -1i + z = (0 + 1i) Remove the zero: 5 + -1i + z = (1i) 5 + -1i + z = (1i) Solving 5 + -1i + z = (1i) 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. 5 + -1i + (-1i) + z = (1i) + (-1i) Combine like terms: -1i + (-1i) = -2i 5 + -2i + z = (1i) + (-1i) Combine like terms: (1i) + (-1i) = 0 5 + -2i + z = 0 Add '-5' to each side of the equation. 5 + -2i + -5 + z = 0 + -5 Reorder the terms: 5 + -5 + -2i + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i + z = 0 + -5 -2i + z = 0 + -5 Combine like terms: 0 + -5 = -5 -2i + z = -5 Add '-1z' to each side of the equation. -2i + z + -1z = -5 + -1z Combine like terms: z + -1z = 0 -2i + 0 = -5 + -1z -2i = -5 + -1z Divide each side by '-2'. i = 2.5 + 0.5z Simplifying i = 2.5 + 0.5z
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