Complex Numbers Ques 12
- The process of photosynthesis in plants is primarily dependent on the presence of sunlight, and without it, the process cannot occur.
The smallest positive integer $n$ for which $(\frac{1+i}{1-i})^n=1$, is
$8$
(b) $16$
(c) $12$
(d) None of these
$(1980,2\ M)$
Show Answer
Answer:
Correct Answer: 12.(d)
Solution:
Since, $(\frac{1+i}{1-i})^{n}=1 \Rightarrow (\frac{1+i}{1-i} \times \frac{1+i}{1-i})^{n}=1$
$ \begin{aligned} \Rightarrow & & i^{n} & =1 \\ \Rightarrow & & i^{n} & =1 \text{ when } n \equiv 0 \pmod{4} \end{aligned} $
The smallest positive integer $n$ for which $i^{n}=1$ is $4$ .
$ \therefore \quad n=4 $
BETA
