91Ó°ÊÓ

In Exercises \(1-8,\) plot the point in the complex plane corresponding to the number. $$(2+i)(1-2 i)$$

Find \(\boldsymbol{u} \cdot \boldsymbol{v}, \boldsymbol{u} \cdot \boldsymbol{u},\) and \(\boldsymbol{v} \cdot \boldsymbol{v}\) $$\mathbf{u}=4 \mathbf{i}-\mathbf{j}, \mathbf{v}=-\mathbf{i}+2 \mathbf{j}$$

Find a vector with the origin as initial point that is equivalent to the vector \(\overrightarrow{P Q}\). $$P=(2,7), Q=(-2,9)$$

In Exercises \(1-8,\) plot the point in the complex plane corresponding to the number. $$2 i\left(3-\frac{5}{2} i\right)$$

Find the dot product when \(u=\langle 4,3\rangle\) \(\boldsymbol{v}=\langle-5,2\rangle,\) and \(\boldsymbol{w}=\langle 4,-1\rangle\) $$\mathbf{u} \cdot(\mathbf{v}+\mathbf{w})$$

Calculate the product by expressing the number in polar form and using DeMoivre's Theorem. Express your answer in the form \(a+b i\). $$\left(\frac{1}{2}+\frac{\sqrt{3}}{2} i\right)^{3}$$

Find a vector with the origin as initial point that is equivalent to the vector \(\overrightarrow{P Q}\). $$P=(-4,-8), Q=(-10,2)$$

In Exercises \(1-8,\) plot the point in the complex plane corresponding to the number. $$\frac{4 i}{3}(-6-3 i)$$

Calculate the product by expressing the number in polar form and using DeMoivre's Theorem. Express your answer in the form \(a+b i\). $$\left(-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2} i\right)^{4}$$

Find a vector with the origin as initial point that is equivalent to the vector \(\overrightarrow{P Q}\). $$P=(-5,6), Q=(-7,-9)$$