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Simplifying z(3 + 2i) = iz + 2 (3 * z + 2i * z) = iz + 2 Reorder the terms: (2iz + 3z) = iz + 2 (2iz + 3z) = iz + 2 Reorder the terms: 2iz + 3z = 2 + iz Solving 2iz + 3z = 2 + iz Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1iz' to each side of the equation. 2iz + -1iz + 3z = 2 + iz + -1iz Combine like terms: 2iz + -1iz = 1iz 1iz + 3z = 2 + iz + -1iz Combine like terms: iz + -1iz = 0 1iz + 3z = 2 + 0 1iz + 3z = 2 Add '-3z' to each side of the equation. 1iz + 3z + -3z = 2 + -3z Combine like terms: 3z + -3z = 0 1iz + 0 = 2 + -3z 1iz = 2 + -3z Divide each side by '1z'. i = 2z-1 + -3 Simplifying i = 2z-1 + -3 Reorder the terms: i = -3 + 2z-1
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