91Ó°ÊÓ

Find the nth roots in polar form. $$16\left(\cos \frac{\pi}{7}+i \sin \frac{\pi}{7}\right) ; \quad n=5$$

Determine whether the given vectors are parallel, orthogonal, or neither. $$2 \mathbf{i}-2 \mathbf{j}, 5 \mathbf{i}+8 \mathbf{j}$$

In Exercises \(17-24,\) sketch the graph of the equation in the complex plane (z denotes a complex number of the form a \(+b i\) ). \(\operatorname{Re}(z)=2\) [The real part of the complex number \(z=a+b i\) is defined to be the number \(a\) and is denoted \(\operatorname{Re}(z) .]\)

Find the nth roots in polar form. $$-1 ; \quad n=5$$

Find the nth roots in polar form. $$1 ; \quad n=7$$

Determine whether the given vectors are parallel, orthogonal, or neither. $$6 i-4 j, 2 i+3 j$$

Find the components of the given vector, where \(\boldsymbol{u}=\boldsymbol{i}-2 \boldsymbol{j}, \boldsymbol{v}=3 \boldsymbol{i}+\boldsymbol{j}, \boldsymbol{w}=-4 \boldsymbol{i}+\boldsymbol{j}\) $$-2 \mathbf{u}+3 \mathbf{v}$$

In Exercises \(17-24,\) sketch the graph of the equation in the complex plane (z denotes a complex number of the form a \(+b i\) ). \(\operatorname{Im}(z)=-5 / 2\) [The imaginary part of \(z=a+b i\) is defined to be the number \(b \text { ( not bi) and is denoted } \operatorname{Im}(z) .]\)

Find the components of the given vector, where \(\boldsymbol{u}=\boldsymbol{i}-2 \boldsymbol{j}, \boldsymbol{v}=3 \boldsymbol{i}+\boldsymbol{j}, \boldsymbol{w}=-4 \boldsymbol{i}+\boldsymbol{j}\) $$\frac{1}{4}(8 u+4 v-w)$$

Find the nth roots in polar form. $$i ; \quad n=5$$