2i^275 + (1+i)^-2. write the expression in the form a+ib
there are only 4 values of i:
i = sqrt(-1)
i^2 = -1
i^3 = -i = -sqrt(-1)
i^4 = 1
2i^275 + (1+i)^-2 lets look at the 2i^275 first. divide 275/4 = 68.75
or 68 3/4 this is the exponent. (i^4)^68 = 1^64 = 1 with the remainder of i^3
or -i
this becomes 2 (-i) or -2i.
replacing in the expression: -2i + (1 + i)^-2
-2i + 1/(1 + i)^2 get a common denominator of (1 + i)^2
[-2i(1 + i)^2 + 1]/(1 + i)^2
[-2i(1 + 2i + i^2) + 1] /(1 + 2i + i^2)
[-2i(1 + 2i -1) + 1]/(1 + 2i -1)
[-2i(2i) + 1]/2i
-4i^2 + 1/ 2i