Question

If

n

is any positive integer, then the value of

4 1 4 1

2

 



n n i i

equals

(a) 1 (b) –1 (c)

i

(d) i​

Answer 1

Question:-

⇒ If n is any positive integer , then the value of $\frac{i^{4n+1} - i^{4n-1} }{2}$equal ?

Answer:-

⇒ $\frac{i^{4n+1} - i^{4n-1} }{2}$

⇒ $\frac{i^{4n} * i^1 - i^{4n} * i^{-1}}{2}$

⇒ $\frac{1* i - \frac{1}{i} }{2}$

⇒ $\frac{i^2 - 1}{2i}$

as i^2 = -1

Therefore:-

⇒ $\frac{-1-1}{2i}$

⇒ $\frac{-2}{2i}$

⇒ $\frac{-1}{i}$

( now multiplying numerator and denomenater by "i" )

We get...

⇒ $\frac{-1}{i} * \frac{i}{i}$

⇒ $\frac{-i}{i^2}$

⇒ $\frac{-i}{-1} ---- ( as i^2 = -1 )$

⇒ $i$

# so our answer to this Question is :-

⇒ $\frac{i^{4n+1} - i^{4n-1} }{2} = i$

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Thank you...........