Complex Numbers

Put the number into polar form $\displaystyle (1/2,\pi/2),$  (abbreviated).

We're finding a root so the number has to be put into its multivalued form, $\displaystyle (1/2,\pi/2+2k\pi), k=0,1,2,...$

$\displaystyle z=(1/2,\pi/2+2k\pi)^{1/2},k=0,1,\\=(1/\sqrt{2},\pi/4+k\pi),k=0,1,\\ =(k=0),(1/\sqrt{2},\pi/4)=(1/2+i/2),\\ \text{or }(k=1),(1/\sqrt{2},5\pi/4)=(-1/2-i/2).$