How do you simplify i44 + i150 – i74 – i109 + i61?

1
We have
##i^1=i##
##i^2= -1##
##i^3 = i^2 xx i = -i##
##i^4 = i^2 xx i^2 =(-1)^2 xx (-1)^2 = 1##
##i^5 = i^4 xx i = 1 xx i =i##
##i^6 = i^4 * i^2 = 1 * -1 = -1##
##i^7 = i^4 * i^3 = 1 * -i = -i ##
##i^8 = i^4 * i^4 = 1 * 1 = 1##
Now
##i^44 = (i^4) ^11 = (1)^11 = 1##
##i^150 = (i^4)^37 * i^2 = i^2 = -1##
##i^74 = (i^4)^18 * i^2 = i^2 = -1##
##i^109 = (i^4)^27 * i^1 = i ##
##i^61 = (i^4)^15 * i^1 = i ##
Finally
##i^44 + i^150 – i^74 – i^109 + i^61##
##=(1) + (-1) – (-1) – (i) + (i)##
##=1 – 1 + 1 – i + i##
##= 1 ##