Question

evaluate the follwing: (1)i457 (2)1/i58

Answer 1

Hi friend!!

(1)

i⁴⁵⁷

=457/4

=1(remainder)

So,i⁴⁵⁷=i

(2) 1/i⁵⁸

=58/4

=2(remainder)

» 1/i²
=1/-1
= -1

So,1/i⁵⁸=-1

Answer 2

This is related to "complex numbers "
we know ,
i⁴ⁿ = 1
i^(4n +1) = i
i^(4n +2) = -1
i^(4n+3) = -i
use this application here,

(1) i^457 = i^(4×114+1) , this is just like i^(4n+1) . so, i^457 = i

(2) 1/i^58 = 1/i^(4×14+2) , this is just like ,
1/i^(4n +2) so, 1/i^58 = 1/-1 = -1