Complex Numbers

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

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(1 + 5i)/2

(1 - 5i)/2

(5 + i)/2

(5 - i)/2

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About This Question

Subject: mathematics
Chapter: complex numbers and quadratic equations
Topic: complex numbers
Difficulty: Medium
Year: 2025

Solution

Correct Answer:

(1 + 5i)/2

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

This medium difficulty mathematics question is from the chapter complex numbers and quadratic equations, covering the topic of complex numbers. It appeared in the 2025 exam.

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