Question

Find the value of i^4n+1-i^4n-1÷2

Answer 1

Answer:

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

Step-by-step explanation:

Formula used:

$i^{4n}=1\:where \:i=\sqrt{-1}$

$\frac{1}{i}=-i$

Now,

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

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

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

$=\frac{i-\frac{1}{i}}{2}$

$=\frac{i-(-i)}{2}$

$=\frac{i+i}{2}$

$=\frac{2i}{2}$

$=i$