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