Complex Numbers

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The conjugate of (3 - 2i)/(1 + i) is

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1. **Rationalize Denominator**: Multiply numerator and denominator by the conjugate of the denominator $(1 - i)$:
   - $\frac{3 - 2i}{1 + i} 	imes \frac{1 - i}{1 - i}$
2. **Calculation**:
   - Numerator: $(3 - 2i)(1 - i) = 3 - 3i - 2i + 2i^2 = 3 - 5i - 2 = 1 - 5i$.
   - Denominator: $(1 + i)(1 - i) = 1^2 - i^2 = 1 + 1 = 2$.
3. **Standard Form**: The value is $\frac{1 - 5i}{2} = \frac{1}{2} - \frac{5}{2}i$.
4. **Find Conjugate**: The conjugate changes the sign of the imaginary part.
   - $	ext{Conjugate} = \frac{1}{2} + \frac{5}{2}i = \frac{1+5i}{2}$.

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