If i squared is -1 than what is i to the 80th?

Algebra Level 2

If i 2 = − 1 i^2 = -1 , what is i 80 i^{80} ?

i i − 1 -1 80 i 80i 1 1

Vedant Srinath by Vedant Srinath , 13, USA

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2 solutions

Richard Desper
Nov 12, 2020

i 2 = − 1 i^2 = -1 , so i 4 = 1 i^4 = 1 . Thus i 4 k = 1 i^{4k} = 1 for any integer value of k k , including k = 20 k=20 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Marvin Kalngan
Nov 14, 2020

i 80 = ( i 2 ) 40 = ( − 1 ) 40 = 1 i^{80}=\left(i^2\right)^{40}=\left( -1 \right)^{40}=\boxed{1}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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