The key to this problem is understanding the definition of the number i and what happens when you raise it to any power.
i2 = -1
Using the product property of exponents,
i3 = i*i2 = -i
i4 = i2*i2 = (-1)(-1) = 1
For any power greater than 4, you can factor out i4, and this factor always reduces to 1.
i5 = i*i4 = i
i6 = i2*i4 = i2 = -1
i7 = i3*i4 = i3 = -i
i8 = i4*i4 = 1*1 = 1
We can simplify this problem by determining what the remainder of the exponent is after factoring out (dividing) all possible 4s from it.
Multiples of 100 are always divisible by 4 (since 100 = 4*25), so we can pull them out
Now you need to find the largest multiple of 4 that is less than your exponent. In this case 4*9=36
And from above,