how to calculate powers of i

√-1  =  i        = i^5        = i^9       = i^13       = ... 

-1     = i²       = i^6        = i^10     = i^14       = ... 

-i     =  i³       = i^7        = i^11     = i^15       = ...

 1    =i^4      = i^8        = i^12      = i^16       = ...

So if the exponent is positive, divide the exponent by 4:

if the remainder is 0, the value is  1

if the remainder is 1, the value is  i

if the remainder is 2, the value is  -1

if the remainder is 3, the value is  -i

For negative exponents:

i^-1  =  1/i x i/i   =   i/i²    =   i/-1   =   -i       =    i^-5     =   ...

i^-2   =   1/i²      =   1/-1   =   -1                  =   i^-6       =   ...

i^-3   =   i/i³       =   i/-i     =   i                     =   i^-7       =   ...

i^-4   =   1/i^4   =   i/1     =   1                     =   i^-8       =   ...

So if the exponent is negative, divide the exponent by 4:

if the remainder is 0, the value is  1

if the remainder is 1, the value is  -i

if the remainder is 2, the value is  -1

if the remainder is 3, the value is  i