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Simplifying 3z + -1i * z + 1 = 10 Multiply i * z 3z + -1iz + 1 = 10 Reorder the terms: 1 + -1iz + 3z = 10 Solving 1 + -1iz + 3z = 10 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 + -1iz + -1 + 3z = 10 + -1 Reorder the terms: 1 + -1 + -1iz + 3z = 10 + -1 Combine like terms: 1 + -1 = 0 0 + -1iz + 3z = 10 + -1 -1iz + 3z = 10 + -1 Combine like terms: 10 + -1 = 9 -1iz + 3z = 9 Add '-3z' to each side of the equation. -1iz + 3z + -3z = 9 + -3z Combine like terms: 3z + -3z = 0 -1iz + 0 = 9 + -3z -1iz = 9 + -3z Divide each side by '-1z'. i = -9z-1 + 3 Simplifying i = -9z-1 + 3 Reorder the terms: i = 3 + -9z-1
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