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Simplifying (4 + i) * z = 2 + -5i Reorder the terms for easier multiplication: z(4 + i) = 2 + -5i (4 * z + i * z) = 2 + -5i Reorder the terms: (iz + 4z) = 2 + -5i (iz + 4z) = 2 + -5i Solving iz + 4z = 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. iz + 5i + 4z = 2 + -5i + 5i Reorder the terms: 5i + iz + 4z = 2 + -5i + 5i Combine like terms: -5i + 5i = 0 5i + iz + 4z = 2 + 0 5i + iz + 4z = 2 Add '-4z' to each side of the equation. 5i + iz + 4z + -4z = 2 + -4z Combine like terms: 4z + -4z = 0 5i + iz + 0 = 2 + -4z 5i + iz = 2 + -4z Reorder the terms: -2 + 5i + iz + 4z = 2 + -4z + -2 + 4z Reorder the terms: -2 + 5i + iz + 4z = 2 + -2 + -4z + 4z Combine like terms: 2 + -2 = 0 -2 + 5i + iz + 4z = 0 + -4z + 4z -2 + 5i + iz + 4z = -4z + 4z Combine like terms: -4z + 4z = 0 -2 + 5i + iz + 4z = 0 The solution to this equation could not be determined.
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