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Simplifying (1 + 2i) * z = 3 + -5i Reorder the terms for easier multiplication: z(1 + 2i) = 3 + -5i (1 * z + 2i * z) = 3 + -5i Reorder the terms: (2iz + 1z) = 3 + -5i (2iz + 1z) = 3 + -5i Solving 2iz + 1z = 3 + -5i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '5i' to each side of the equation. 2iz + 5i + 1z = 3 + -5i + 5i Reorder the terms: 5i + 2iz + 1z = 3 + -5i + 5i Combine like terms: -5i + 5i = 0 5i + 2iz + 1z = 3 + 0 5i + 2iz + 1z = 3 Add '-1z' to each side of the equation. 5i + 2iz + 1z + -1z = 3 + -1z Combine like terms: 1z + -1z = 0 5i + 2iz + 0 = 3 + -1z 5i + 2iz = 3 + -1z Reorder the terms: -3 + 5i + 2iz + z = 3 + -1z + -3 + z Reorder the terms: -3 + 5i + 2iz + z = 3 + -3 + -1z + z Combine like terms: 3 + -3 = 0 -3 + 5i + 2iz + z = 0 + -1z + z -3 + 5i + 2iz + z = -1z + z Combine like terms: -1z + z = 0 -3 + 5i + 2iz + z = 0 The solution to this equation could not be determined.
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