Complex current density of sphere confusion

Hello,

I am a bit confused on how to get this into the proper form,

$$
\begin{eqnarray}
\vec{J} &=& \vec{v}\rho \\
&=& (\vec{\omega} \times \vec{r}')\rho_o \Theta(R-r') \\
&=& \omega r' \sin(\theta')\rho_o \Theta(R-r')[\cos(\phi')\hat{y} - \sin(\phi')\hat{x}] \\
&=& \vdots \\
J_x + i J_y &=& -i \sqrt{\frac{3}{2 \pi}}\frac{q \omega r'}{R^3}\Theta(R-r')Y_{1,1}(\theta', \phi')
\end{eqnarray}
$$

I have tried expanding and such but the algebra does not work out. What am I missing conceptually? I know that the term in the brackets should equate to,

$$
[\cdots] = i e^{i \phi'}
$$

which I can then do some algebra to get the result into spherical harmonics. How does the term in brackets equate to [itex]i e^{i \phi'}?[/itex] Do I simply multiply the [itex]\hat{y}[/itex] term by i?

Hope you can shed some light on this matter!

EDIT

Yep, turns out I simply multiple [itex] \hat{y} [/itex] term by i. I just missed a minus sign! Sorry for the silly post!