CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations1 Mark
Question
The number $\frac{(1-\text{i})^3}{1-\text{i}^3}$ is equal to __________.
✓
Answer
The number $\frac{(1-\text{i})^3}{1-\text{i}^3}$ is equal to -2. Solution: $\frac{(1-\text{i})^3}{1-\text{i}^3}=\frac{(1-\text{i})^3}{(1-\text{i})(1+\text{i}+\text{i}^2)}=\frac{(1-\text{i})^2}{\text{i}}$ $=\frac{1+\text{i}^2-2\text{i}}{\text{i}}=\frac{-2\text{i}}{\text{i}}=-2$
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