Roots of Unity

1. The non-real number i raised to what power is one? (Of course, when raised to the zeroth power it is one, but there are other powers as well.)

2. Compute the square of:2^{-1/2}(1 + i)

3. Compute the cube of: 2^{-1/2}(1 + i)

4. What power of 2^{-1/2}(1 + i) is one? In other words, 2^{-1/2}(1 + i) raised to what power is one?

5. Compute the square of: 2^{-1/2}(1 – i)