Answer
$$\mathbf{u}+\mathbf{v}=\left(1+\frac{3\sqrt{2}}{2},\frac{3\sqrt{2}}{2}\right)$$
Work Step by Step
$\|\mathbf{u}\|=1\hspace{5mm}\theta_u=0^\circ$
$\|\mathbf{v}\|=3\hspace{5mm}\theta_v=45^\circ$
$u_x=\|\mathbf{u}\|\cos{\theta_u}=1\times\cos{0}=1$
$u_y=\|\mathbf{u}\|\sin{\theta_u}=1\times\sin{0}=0$
$v_x=\|\mathbf{v}\|\cos{\theta_v}=3\times\cos{45}=\frac{3\sqrt{2}}{2}$
$v_y=\|\mathbf{v}\|\sin{\theta_v}=3\times\sin{45}=\frac{3\sqrt{2}}{2}$
Therefore,
$$\mathbf{u}+\mathbf{v}=\left(1+\frac{3\sqrt{2}}{2},\frac{3\sqrt{2}}{2}\right)$$
