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Simplifying (z + 1)(1 + -1i) = 2 + 3i Reorder the terms: (1 + z)(1 + -1i) = 2 + 3i Multiply (1 + z) * (1 + -1i) (1(1 + -1i) + z(1 + -1i)) = 2 + 3i ((1 * 1 + -1i * 1) + z(1 + -1i)) = 2 + 3i ((1 + -1i) + z(1 + -1i)) = 2 + 3i (1 + -1i + (1 * z + -1i * z)) = 2 + 3i Reorder the terms: (1 + -1i + (-1iz + 1z)) = 2 + 3i (1 + -1i + (-1iz + 1z)) = 2 + 3i (1 + -1i + -1iz + 1z) = 2 + 3i Solving 1 + -1i + -1iz + 1z = 2 + 3i 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. 1 + -1i + -1iz + -3i + 1z = 2 + 3i + -3i Reorder the terms: 1 + -1i + -3i + -1iz + 1z = 2 + 3i + -3i Combine like terms: -1i + -3i = -4i 1 + -4i + -1iz + 1z = 2 + 3i + -3i Combine like terms: 3i + -3i = 0 1 + -4i + -1iz + 1z = 2 + 0 1 + -4i + -1iz + 1z = 2 Add '-1' to each side of the equation. 1 + -4i + -1iz + -1 + 1z = 2 + -1 Reorder the terms: 1 + -1 + -4i + -1iz + 1z = 2 + -1 Combine like terms: 1 + -1 = 0 0 + -4i + -1iz + 1z = 2 + -1 -4i + -1iz + 1z = 2 + -1 Combine like terms: 2 + -1 = 1 -4i + -1iz + 1z = 1 Add '-1z' to each side of the equation. -4i + -1iz + 1z + -1z = 1 + -1z Combine like terms: 1z + -1z = 0 -4i + -1iz + 0 = 1 + -1z -4i + -1iz = 1 + -1z Reorder the terms: -1 + -4i + -1iz + z = 1 + -1z + -1 + z Reorder the terms: -1 + -4i + -1iz + z = 1 + -1 + -1z + z Combine like terms: 1 + -1 = 0 -1 + -4i + -1iz + z = 0 + -1z + z -1 + -4i + -1iz + z = -1z + z Combine like terms: -1z + z = 0 -1 + -4i + -1iz + z = 0 The solution to this equation could not be determined.
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