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What is the value of i^2018+i^2019+i^2020+i^2021? Single correct option
What is the value of
i 2018 + i 2019 + i 2020 + i 2021 i^{2018}+i^{2019}+i^{2020}+i^{2021} i 2018 + i 2019 + i 2020 + i 2021 ?
A. − 2 -2 − 2 B. 2 i 2i 2 i C. 1 + i 1+i 1 + i D. 0 Show answer and solution Answer: (D) 0
Four consecutive powers of
i i i always sum to zero:
i n ( 1 + i − 1 − i ) = 0 i^{n}(1+i-1-i)=0 i n ( 1 + i − 1 − i ) = 0 . Explicitly
i 2018 = − 1 i^{2018}=-1 i 2018 = − 1 ,
i 2019 = − i i^{2019}=-i i 2019 = − i ,
i 2020 = 1 i^{2020}=1 i 2020 = 1 ,
i 2021 = i i^{2021}=i i 2021 = i , sum
= 0 =0 = 0 . Reducing the exponent modulo 4 is the key step.
Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake