Question

if n is any positive integer then write the value of i^4n+1-i^4n-1÷2​

Answer 1

Answer:

i or iota

Step-by-step explanation:

$\frac{ {i}^{4n + 1} - {i}^{4n - 1} }{2} \\ = \frac{ {i}^{4n} \times i - ( {i}^{4n} \times \frac{1}{i} )}{2} \\ = \frac{i - \frac{1}{i} }{2} \\ = \frac{i - ( - i)}{2} \\ = \frac{2i}{2} \\ = i$

We know that (i)^2=-1, so (i)^4=1.

Hence, the answer is i.

Thank you