Question

Value of i^-2021 is equal to

Answer 1

Answer:

Step-by-step explanation:

We have,

${i}^{-2021}$

$=\left(\dfrac{1}{i}\right)^{2021}$

$=\left(\dfrac{1\times\,i}{i\times\,i}\right)^{2021}$

$=\left(\dfrac{i}{{i}^{2}}\right)^{2021}$

$=\left(\dfrac{i}{-1}\right)^{2021}$

$=\left(-i\right)^{2021}$

Since 2021 is an odd number, so,

$=-\left(i\right)^{2021}$

$=-\left(i\right)^{2020+1}$

$=-\left(i\right)^{4\times505}\cdot\,i$

$\tt{We\,\,know\,,\,\,i^{4n}=1}$

So,

$=-1\cdot\,i$

$=-i$