Ends at i 20 i^{20}

Algebra Level 4

i i 2 i 3 i 4 … i 20 = ? \large i ~ i^2 i^3 i^4 \ldots i^{20}= ?

Notation: i i denotes the imaginary unit.

i i 0 0 i 2 i^2 − i -i 20 i 20i None of these 1 1

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Hana Wehbi
Nov 5, 2017

i i 2 i 3 i 4 … i 20 = i 1 + 2 + 3 + ⋯ + 20 = i 20 × 21 2 = i 210 = i ( 210 m o d 4 ) = i 2 , I took mod 4 because i 4 = 1. \large i ~ i^2 i^3 i^4 \ldots i^{20}= i ^{1+2+3+\dots+20} = i^{\frac {20\times 21}{2}} = i ^ {210}= i^{(210 \mod 4)}= i^2\text{, I took mod 4 because } i^4 =1.

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