Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers and Quadratic Equations3 Marks
Question
What is the conjugate of $\frac{2-\text{i}}{(1-2\text{i})^2}$
✓
Answer
We have $\text{z}=\frac{2-\text{i}}{(1-2\text{i})^2}$ $\text{z}=\frac{2-\text{i}}{1+4\text{i}^2-4\text{i}}=\frac{2-\text{i}}{1-4-4\text{i}}=\frac{2-\text{i}}{-3-4\text{i}}$ $=\frac{(2-\text{i})}{-(3+4\text{i})}=-\Big[\frac{(2-\text{i})(3-4)}{(3+4\text{i})(3-4\text{i})}\Big]$ $=-\Big(\frac{6-8\text{i}-3\text{i}+4\text{i}^2}{9+16}\Big)=-\frac{(-11\text{i}+2)}{25}$ $=\frac{-1}{25}(2-11\text{i})=\frac{1}{25}(-2+11\text{i})$ $\therefore\ \bar{\text{z}}=\frac{1}{25}(-2-11\text{i})=\frac{-2}{25}-\frac{11}{25}\text{i}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.