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