Find the value of
i^2020 + i^ 2021 + i^ 2022 + i^2023
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Answer:
what is the value of i
i can't understand the question
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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.
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