Chapter 7

Find the indicated dot product. $$(4,-2) \cdot(3,5)$$

Plot indicated point in a polar coordinate system. $$\left(3, \frac{5 \pi}{6}\right)$$

Find the product \(z_{1} z_{2}\) and express it in rectangular form. $$z_{1}=4\left(\cos 40^{\circ}+i \sin 40^{\circ}\right) \text { and } z_{2}=3\left(\cos 80^{\circ}+i \sin 80^{\circ}\right)$$

Graph each complex number in the complex plane. $$7+8 i$$

Find the magnitude of the vector \(\mathbf{A B} .\) $$A=(2,7) \text { and } B=(5,9)$$

Find the indicated dot product. $$(7,8) \cdot(2,-1)$$

Plot indicated point in a polar coordinate system. $$\left(2, \frac{5 \pi}{4}\right)$$

Find the product \(z_{1} z_{2}\) and express it in rectangular form. $$z_{1}=2\left(\cos 100^{\circ}+i \sin 100^{\circ}\right) \text { and } z_{2}=5\left(\cos 50^{\circ}+i \sin 50^{\circ}\right)$$

Graph each complex number in the complex plane. $$3+5 i$$

Find the magnitude of the vector \(\mathbf{A B} .\) $$A=(-2,3) \text { and } B=(3,-4)$$

Find the indicated dot product. $$\langle-5,6\rangle \cdot\langle 3,2\rangle$$

Plot indicated point in a polar coordinate system. $$\left(4, \frac{11 \pi}{6}\right)$$

Find the product \(z_{1} z_{2}\) and express it in rectangular form. $$z_{1}=4\left(\cos 80^{\circ}+i \sin 80^{\circ}\right) \text { and } z_{2}=2\left(\cos 145^{\circ}+i \sin 145^{\circ}\right)$$

Graph each complex number in the complex plane. $$-2-4 i$$

Find the magnitude of the vector \(\mathbf{A B} .\) $$A=(4,1) \text { and } B=(-3,0)$$

Find the indicated dot product. $$(6,-3) \cdot(2,1)$$

Plot indicated point in a polar coordinate system. $$\left(1, \frac{2 \pi}{3}\right)$$

Find the product \(z_{1} z_{2}\) and express it in rectangular form. $$z_{1}=3\left(\cos 130^{\circ}+i \sin 130^{\circ}\right) \text { and } z_{2}=4\left(\cos 170^{\circ}+i \sin 170^{\circ}\right)$$

Graph each complex number in the complex plane. $$-3-2 i$$

Find the magnitude of the vector \(\mathbf{A B} .\) $$A=(-1,-1) \text { and } B=(2,-5)$$

Find the indicated dot product. $$(-7,-4) \cdot\langle-2,-7\rangle$$

Plot indicated point in a polar coordinate system. $$\left(-2, \frac{\pi}{6}\right)$$

Find the product \(z_{1} z_{2}\) and express it in rectangular form. $$z_{1}=2\left(\cos 10^{\circ}+i \sin 10^{\circ}\right) \text { and } z_{2}=4\left(\cos 80^{\circ}+i \sin 80^{\circ}\right)$$

Find the magnitude of the vector \(\mathbf{A B} .\) $$A=(0,7) \text { and } B=(-24,0)$$

Find the indicated dot product. $$(5,-2) \cdot\langle-1,-1\rangle$$

Plot indicated point in a polar coordinate system. $$\left(-4, \frac{7 \pi}{4}\right)$$

Find the product \(z_{1} z_{2}\) and express it in rectangular form. $$z_{1}=3\left(\cos 190^{\circ}+i \sin 190^{\circ}\right) \text { and } z_{2}=5\left(\cos 80^{\circ}+i \sin 80^{\circ}\right)$$

Graph each complex number in the complex plane. $$7$$

Find the magnitude of the vector \(\mathbf{A B} .\) $$A=(-2,1) \text { and } B=(4,9)$$

Find the indicated dot product. $$\langle\sqrt{3},-2\rangle \cdot\langle 3 \sqrt{3},-1\rangle$$

Plot indicated point in a polar coordinate system. $$\left(-4,270^{\circ}\right)$$

Find the product \(z_{1} z_{2}\) and express it in rectangular form. $$z_{1}=\sqrt{3}\left[\cos \left(\frac{\pi}{12}\right)+i \sin \left(\frac{\pi}{12}\right)\right] \text { and } z_{2}=\sqrt{27}\left[\cos \left(\frac{\pi}{6}\right)+i \sin \left(\frac{\pi}{6}\right)\right]$$

Graph each complex number in the complex plane. $$-3 i$$

Find the magnitude and direction angle of the given vector. $$\mathbf{u}=\langle 3,8\rangle$$

Find the indicated dot product. $$\langle 4 \sqrt{2}, \sqrt{7}\rangle \cdot\langle-\sqrt{2},-\sqrt{7}\rangle$$

Plot indicated point in a polar coordinate system. $$\left(3,135^{\circ}\right)$$

Find the product \(z_{1} z_{2}\) and express it in rectangular form. $$z_{1}=\sqrt{5}\left[\cos \left(\frac{\pi}{15}\right)+i \sin \left(\frac{\pi}{15}\right)\right] \text { and } z_{2}=\sqrt{5}\left[\cos \left(\frac{4 \pi}{15}\right)+i \sin \left(\frac{4 \pi}{15}\right)\right]$$

Graph each complex number in the complex plane. $$-5 i$$

Find the magnitude and direction angle of the given vector. $$\mathbf{u}=\langle 4,7\rangle$$

Find the indicated dot product. $$\langle 5, a\rangle \cdot\langle-3 a, 2\rangle$$

Plot indicated point in a polar coordinate system. $$\left(4,225^{\circ}\right)$$

Find the product \(z_{1} z_{2}\) and express it in rectangular form. $$z_{1}=4\left[\cos \left(\frac{3 \pi}{8}\right)+i \sin \left(\frac{3 \pi}{8}\right) \text { and } z_{2}=3\left[\cos \left(\frac{\pi}{8}\right)+i \sin \left(\frac{\pi}{8}\right)\right]\right.$$

Express each complex number in polar form. $$1-i$$

Find the magnitude and direction angle of the given vector. $$u=(5,-1)$$

Find the indicated dot product. $$(4 x, 3 y) \cdot(2 y,-5 x)$$

Plot indicated point in a polar coordinate system. $$\left(-2,60^{\circ}\right)$$

Find the product \(z_{1} z_{2}\) and express it in rectangular form. $$z_{1}=6\left[\cos \left(\frac{2 \pi}{9}\right)+i \sin \left(\frac{2 \pi}{9}\right) \text { and } z_{2}=5\left[\cos \left(\frac{\pi}{9}\right)+i \sin \left(\frac{\pi}{9}\right)\right]\right.$$

Express each complex number in polar form. $$2+2 i$$

Find the magnitude and direction angle of the given vector. $$\mathbf{u}=\langle-6,-2\rangle$$

Find the indicated dot product. $$\langle 0.8,-0.5\rangle \cdot\langle 2,6\rangle$$