91Ó°ÊÓ

Fill in the blanks. The ____ ____ of a complex number \(z-a+b i\) is given by \(z-r(\cos \theta+i \sin \theta),\) where \(r\) is the ____ of \(z\) and \(\theta\) is the _____ of \(z.\)

If \(\theta\) is the angle between two nonzero vectors \(\mathbf{u}\) and \(\mathbf{v},\) then \(\cos \theta=\) __________.

The two basic vector operations are scalar _____ and vector _____.

Use the Law of sines to solve the triangle. Round your answers to two decimal places. \(A=36^{\circ}, \quad a=8, \quad b=5\)

Find the component form and magnitude of the vector v. $$\begin{array}{cc}\text{Initial Point} && \text{Terminal Point} \\ (-2,7) && (5,-17) \end{array}$$

Find the component form and magnitude of the vector v. $$\begin{array}{cc}\text{Initial Point} && \text{Terminal Point} \\ (1,11) && (9,3) \end{array}$$

Use the Law of cosines to solve the triangle. Round your answers to two decimal places. $$C=101^{\circ}, \quad a=\frac{3}{8}, \quad b=\frac{3}{4}$$

Use the dot product to find the magnitude of u. $$\mathbf{u}=\langle-8,15\rangle$$

Writing a Complex Number in Standard Form Write the standard form of the complex number. Then represent the complex number graphically. $$\sqrt{8}\left(\cos 225^{\circ}+i \sin 225^{\circ}\right)$$

Graph the vectors and find the degree measure of the angle \(\theta\) between the vectors. $$\begin{aligned}&\mathbf{u}=5 \mathbf{i}+5 \mathbf{j}\\\&\mathbf{v}=-8 \mathbf{i}+8 \mathbf{j}\end{aligned}$$