Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers and Quadratic Equations3 Marks
Question
Find the modulus and argument of the complex number $\frac{1+i}{1-i}$
✓
Answer
We have $\frac{1+i}{1-i}=\frac{1+i}{1-i} \times \frac{1+i}{1+i}=\frac{1-1+2 i}{1+1}$ = i = 0 + i Now, let us put 0 = r cos $\theta$, 1 = r sin $\theta$ Squaring and adding, r2 = 1 i.e., r = 1 so that cos $\theta$ = 0, sin $\theta$ = 1 Therefore, $\theta = \frac {\pi}{2}$ Hence, the modulus of $\frac {1+i}{1-i}$ is 1 and the argument is $\frac {\pi}2.$
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