NDA 2023 Maths · Mathematics · Complex Numbers and Quadratic Equations · hard

The value of i+i^2+i^3+…+i^2023 is

Single correct option

The value of

i+i^2+i^3+\cdots+i^{2023}

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Answer: (D) $-1$

Four consecutive powers of

i

sum to

i-1-i+1=0

. The first

2020

terms form

505

such groups and contribute

0

. The remaining terms are

i^{2021}+i^{2022}+i^{2023}=i+(-1)+(-i)=-1

. The answer

0

results from wrongly assuming 2023 terms split evenly into groups of four.

Original question written in the NDA 2023 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