91Ó°ÊÓ

Represent the complex number graphically, and find the trigonometric form of the number. $$2+2 i$$

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=4 \mathbf{j}\\\ &\mathbf{v}=-9 \mathbf{i} \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$\sqrt{3}+i$$

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=\cos \left(\frac{\pi}{3}\right) \mathbf{i}+\sin \left(\frac{\pi}{3}\right) \mathbf{j}\\\ &\mathbf{v}=\cos \left(\frac{3 \pi}{4}\right) \mathbf{i}+\sin \left(\frac{3 \pi}{4}\right) \mathbf{j} \end{aligned}$$

Use the Law of Sines to solve the triangle. If two solutions exist, find both. \(A=58^{\circ}, \quad a=11.4, \quad b=12.8\)

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=\cos \left(\frac{\pi}{4}\right) \mathbf{i}+\sin \left(\frac{\pi}{4}\right) \mathbf{j}\\\ &\mathbf{v}=\cos \left(\frac{2 \pi}{3}\right) \mathbf{i}+\sin \left(\frac{2 \pi}{3}\right) \mathbf{j} \end{aligned}$$

Use the Law of Sines to solve the triangle. If two solutions exist, find both. \(A=58^{\circ}, \quad a=4.5, \quad b=12.8\)

Represent the complex number graphically, and find the trigonometric form of the number. $$1-\sqrt{3} i$$

Represent the complex number graphically, and find the trigonometric form of the number. $$1+i$$

Graph the vectors and find the degree measure of the angle between the vectors. $$\begin{aligned} &\mathbf{u}=2 \mathbf{i}-4 \mathbf{j}\\\ &\mathbf{v}=3 \mathbf{i}-5 \mathbf{j} \end{aligned}$$