91Ó°ÊÓ

Writing a Complex Number in Standard Form In Exercises \(31-40\) , write the standard form of the complex number. Then represent the complex number graphically. $$\frac{9}{4}\left(\cos \frac{3 \pi}{4}+i \sin \frac{3 \pi}{4}\right)$$

Finding the Angle Between Two Vectors In Exercises \(31-40,\) find the angle \(\theta\) between the vectors. $$\mathbf{u}=2 \mathbf{i}-\mathbf{j}$$ $$\mathbf{v}=6 \mathbf{i}+4 \mathbf{j}$$

Vector Operations In Exercises 31-38, find (a) \(\mathbf{u}+\mathbf{v}\) . (b) \(\mathbf{u}-\mathbf{v},\) and \((\mathbf{c}) 2 \mathbf{u}-3 \mathbf{v} .\) Then sketch each resultant vector. $$\mathbf{u}=\mathbf{i}+\mathbf{j}, \mathbf{v}=2 \mathbf{i}-3 \mathbf{j}$$

Vector Operations In Exercises 31-38, find (a) \(\mathbf{u}+\mathbf{v}\) . (b) \(\mathbf{u}-\mathbf{v},\) and \((\mathbf{c}) 2 \mathbf{u}-3 \mathbf{v} .\) Then sketch each resultant vector. $$\mathbf{u}=-2 \mathbf{i}+\mathbf{j}, \mathbf{v}=3 \mathbf{j}$$

Writing a Complex Number in Standard Form In Exercises \(31-40\) , write the standard form of the complex number. Then represent the complex number graphically. $$6\left(\cos \frac{5 \pi}{12}+i \sin \frac{5 \pi}{12}\right)$$

Finding the Angle Between Two Vectors In Exercises \(31-40,\) find the angle \(\theta\) between the vectors. $$\mathbf{u}=-6 \mathbf{i}-3 \mathbf{j}$$ $$\mathbf{v}=-8 \mathbf{i}+4 \mathbf{j}$$

Finding the Angle Between Two Vectors In Exercises \(31-40,\) find the angle \(\theta\) between the vectors. $$\begin{aligned} \mathbf{u} &=5 \mathbf{i}+5 \mathbf{j} \\ \mathbf{v} &=-6 \mathbf{i}+6 \mathbf{j} \end{aligned}$$

Using Heron's Area Formula use Heron's Area Formula to find the area of the triangle. $$ a=8, \quad b=12, \quad c=17 $$

Writing a Complex Number in Standard Form In Exercises \(31-40\) , write the standard form of the complex number. Then represent the complex number graphically. $$7(\cos 0+i \sin 0)$$

Vector Operations In Exercises 31-38, find (a) \(\mathbf{u}+\mathbf{v}\) . (b) \(\mathbf{u}-\mathbf{v},\) and \((\mathbf{c}) 2 \mathbf{u}-3 \mathbf{v} .\) Then sketch each resultant vector. $$\mathbf{u}=2 \mathbf{i}, \mathbf{v}=\mathbf{j}$$