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Simplifying (1 + 2i) * z = 3z + -1i Reorder the terms for easier multiplication: z(1 + 2i) = 3z + -1i (1 * z + 2i * z) = 3z + -1i Reorder the terms: (2iz + 1z) = 3z + -1i (2iz + 1z) = 3z + -1i Reorder the terms: 2iz + 1z = -1i + 3z Solving 2iz + 1z = -1i + 3z Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. 2iz + i + 1z = -1i + i + 3z Reorder the terms: i + 2iz + 1z = -1i + i + 3z Combine like terms: -1i + i = 0 i + 2iz + 1z = 0 + 3z i + 2iz + 1z = 3z Add '-1z' to each side of the equation. i + 2iz + 1z + -1z = 3z + -1z Combine like terms: 1z + -1z = 0 i + 2iz + 0 = 3z + -1z i + 2iz = 3z + -1z Combine like terms: 3z + -1z = 2z i + 2iz = 2z Combine like terms: 2z + -2z = 0 i + 2iz + -2z = 0 The solution to this equation could not be determined.
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