91Ó°ÊÓ

Write the complex number in polar form with argument \(\theta\) between 0 and \(2 \pi\). $$1+i$$

Sketch the graph of the polar equation. $$r=-3(1+\sin \theta)$$

(a)\( Calculate proj \)u\(, (b) Resolve \)u\( into \)u_{1}\( and \)u_{2}\( where \)\mathbf{u}_{1}\( is parallel to \)\mathbf{v}\( and \)\mathbf{u}_{2}\( is orthogonal to \)\mathbf{v}$ $$\mathbf{u}=\langle 1,2\rangle, \quad \mathbf{v}=\langle 1,-3\rangle$$

Find \(|\mathbf{u}|,|\mathbf{v}|,|2 \mathbf{u}|,\left|\frac{1}{2} \mathbf{v}\right|,|\mathbf{u}+\mathbf{v}|,|\mathbf{u}-\mathbf{v}|,\) and\(|\mathbf{u}|-|\mathbf{v}|\). $$\mathbf{u}=\langle 10,-1\rangle, \quad \mathbf{v}=\langle- 2,-2\rangle$$

Sketch the graph of the polar equation. $$r=\cos \theta-1$$

Find the rectangular coordinates for the point whose polar coordinates are given. $$(6,2 \pi / 3)$$

Write the complex number in polar form with argument \(\theta\) between 0 and \(2 \pi\). $$1+\sqrt{3} i$$

(a)\( Calculate proj \)u\(, (b) Resolve \)u\( into \)u_{1}\( and \)u_{2}\( where \)\mathbf{u}_{1}\( is parallel to \)\mathbf{v}\( and \)\mathbf{u}_{2}\( is orthogonal to \)\mathbf{v}$ $$\mathbf{u}=\langle 11,3\rangle, \quad \mathbf{v}=\langle- 3,-2\rangle$$

Sketch the graph of the polar equation. $$r=\theta, \quad \theta \geq 0 \quad \text { (spiral) }$$

Find the rectangular coordinates for the point whose polar coordinates are given. $$(\sqrt{2},-\pi / 4)$$