What is negative i raised to the one half power?

Answer 1

There are two square roots of i: (-1/square root 2)(1+i) and (1/square root 2)(1+i)

so these are i to the one half power. Now to find -i to the one half power, multiply either of these by i, since i2 is -1.

So (-i/square root 2)(1+i) and (i/square root 2)(1+i) are the square roots of -i.

Verify this by direct multiplication.