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