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