The value of -1+i31-i30 is

we know that -1+i3=2ω where ω is cube root of  unityHence, −1+i330=230ω30=230   since ω3=1And (1-i)2=1+i2-2i=-2i Hence, (1-i)30=(-2i)15=-215(-i)=215i Therefore, -1+i31-i30=230215i=215(-i)    since i15=i43i3=-i