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Complex Numbers — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers3 Marks
Question
Find the conjugates of the following complex numbers:
$\frac{1}{1+\text{i}}$
✓

Answer

Let $\text{z}=\frac{1}{1+\text{i}}$
$=\frac{1}{1+\text{i}}\times\frac{(1-\text{i})}{1-\text{i}}$
$=\frac{1+\text{i}}{1^2+1^2}$
$=\frac{1-\text{i}}{2}$
$\therefore\bar{\text{z}}=\frac{1-\text{i}}{2}$
$=\frac{1}{2}+\frac{1}{2}\text{i}$

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