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Simplifying (1 + -1i) * z + (2 + i) * z = 2 + 2i Reorder the terms for easier multiplication: z(1 + -1i) + (2 + i) * z = 2 + 2i (1 * z + -1i * z) + (2 + i) * z = 2 + 2i Reorder the terms: (-1iz + 1z) + (2 + i) * z = 2 + 2i (-1iz + 1z) + (2 + i) * z = 2 + 2i Reorder the terms for easier multiplication: -1iz + 1z + z(2 + i) = 2 + 2i -1iz + 1z + (2 * z + i * z) = 2 + 2i Reorder the terms: -1iz + 1z + (iz + 2z) = 2 + 2i -1iz + 1z + (iz + 2z) = 2 + 2i Reorder the terms: -1iz + iz + 1z + 2z = 2 + 2i Combine like terms: -1iz + iz = 0 0 + 1z + 2z = 2 + 2i 1z + 2z = 2 + 2i Combine like terms: 1z + 2z = 3z 3z = 2 + 2i Solving 3z = 2 + 2i Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Divide each side by '3'. z = 0.6666666667 + 0.6666666667i Simplifying z = 0.6666666667 + 0.6666666667i
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