Multiply by a phase

Compute $w=(1+i)\,e^{i\pi/4}$ and enter it in Cartesian form $w=a+ib$ (as a complex number). You may work in Cartesian form with Euler's formula $e^{i\theta}=\cos\theta+i\sin\theta$, or in polar form using $r_1e^{i\theta_1}\,r_2e^{i\theta_2}=r_1r_2\,e^{i(\theta_1+\theta_2)}$. Answers are accepted within $10^{-3}$.