jmc

Not wanting to multiply out a product with 46 factors, we first see what happens when we square $(1+i)/\sqrt{2}$. We have $${\left(\frac{1+i}{\sqrt{2}}\right)}^2=\frac{1+2i+i^2}{(\sqrt{2}{)}^2}=\frac{1+2i-1}{2}=i.$$ So ${\left(\frac{1+i}{\sqrt{2}}\right)}^{46}={\left({\left(\frac{1+i}{\sqrt{2}}\right)}^2\right)}^{23}=i^{23}=(i^{20})(i^3)=i^3=\boxed{-i}$.