Question

Find the value of

i^2020 + i^ 2021 + i^ 2022 + i^2023​

Answer 1

Answer:

what is the value of i

i can't understand the question

Answer 2

Given:

i²⁰²⁰+ i²⁰²¹ + i²⁰²² + i²⁰²³

To Find:

Value of above expression

Solution:

We know that,

i = √-1

i² = -1

i³ = -i

i⁴ = 1

The expression is  i²⁰²⁰+ i²⁰²¹ + i²⁰²² + i²⁰²³

i²⁰²⁰ can be written as i⁴⁽⁵⁰⁵⁾ = 1⁵⁰⁵ = 1

i²⁰²¹ can be written as i⁴⁽⁵⁰⁵⁾ . i¹ = 1⁵⁰⁵. i¹ = 1 . i = i

i²⁰²² can be written as i⁴⁽⁵⁰⁵⁾. i² = 1⁵⁰⁵. -1  = - 1

i²⁰²³ can be written as i⁴⁽⁵⁰⁵⁾. i³ = 1⁵⁰⁵. i³  = 1 . i³ = -i

put value in the above expression:

i²⁰²⁰+ i²⁰²¹ + i²⁰²² + i²⁰²³

= 1 + i - 1 - i

= 0

Hence, the value of the expression is 0.