How do you simplify #i^(-43)+i^(-32)# ?
1 Answer
Apr 11, 2017
Explanation:
Look at the first few non-negative powers of
#i^0 = 1#
#i^1 = i#
#i^2 = -1#
#i^3 = -i#
#i^4 = 1#
Basically this pattern:
In terms of angles, multiplying by
So in general we can write:
#{ (i^(4n) = 1), (i^(4n+1) = i), (i^(4n+2) = -1), (i^(4n+3) = -i) :}#
which holds for any integer
Now:
#-43 = -44+1 = 4(-11)+1#
#-32 = -32+0 = 4(-8)+0#
So:
#i^(-43)+i^(-32) = i+1#