T&T6: Ex3.7 Polar Form of a Complex Number

What quadrant would the point in polar form land in?
4 ( cos π /3 + i sin π /3)

• Quadrant 4
• Quadrant 1
• Quadrant 2
• Quadrant 3

Find the magnitude of the complex number. Also state which quadrant the point lies in.
 $-4+i$  

•  $\sqrt{17}$ , Quadrant 2

•  $\sqrt{17}$ , Quadrant 3

• 4, Quadrant 2

• -1, Quadrant 3

Express this complex number in rectangular form.
 $4\left(\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}\right)$  

•  $2+2\sqrt{3}i$  

•  $-2+\frac{4\sqrt{3}}{2}i$  

•  $-2-\frac{4\sqrt{3}}{2}i$  

•  $-2+2\sqrt{3}i$  

Express the complex number in polar form.
 $-2+6i$  

•  $2\sqrt{10}\left(\cos\left(108.43\right)+i\sin\left(108.43\right)\right)$  

•  $2\sqrt{10}\left(\cos\left(-71.56\right)+i\sin\left(-71.56\right)\right)$ 

•  $\sqrt{40}\left(\cos\left(288.43\right)+i\sin\left(288.43\right)\right)$ 

•  $\sqrt{40}\left(\cos\left(108.43\right)+i\sin\left(108.43\right)\right)$ 

Find the magnitude of the complex number. Also state the quadrant in which the point lies. 
 $7-i$  

•  $\sqrt{50}$ , Quadrant 1

•  $\sqrt{50}$ , Quadrant 4

•  $\sqrt{49}$ , Quadrant 4

•  $5\sqrt{2}$ , Quadrant 4

•  $5\sqrt{2}$ , Quadrant 1

Write the complex number $-3i$ in polar form

•  $3\left(\cos\left(\frac{3\pi}{2}\right)+i\sin\left(\ \frac{3\pi}{2}\right)\right)$ 

•  $3\left(\cos\left(\frac{\pi}{2}\right)+i\sin\left(\frac{\pi}{2}\right)\right)$ 

•  $9\left(\cos\left(\frac{3\pi}{2}\right)+i\sin\left(\frac{3\pi}{2}\right)\right)$ 

•  $3\left(\cos\left(2\pi\right)+i\sin\left(2\pi\right)\right)$ 

Write the complex number in rectangular form

6 (cos 330 + i sin 330)

• $3\sqrt{3}+3i$

• $-3\sqrt{3}+3i$

• $3\sqrt{3}-3i$

• $-3\sqrt{3}-3i$

Write the complex number in rectangular form

9(cos 180 + i sin180)

• -9i

• -9

• 9i

• 0

 $8\left(\cos\ \frac{\pi}{6}+\ i\ \sin\ \frac{\pi}{6}\right)$  
Write the complex number in rectangular form

•  $4\sqrt{3}+4i$  

•  $4+4i\sqrt{3}$  

•  $4\sqrt{3}-4i$  

•  $-4\sqrt{3}+4i$  

4i

Write the complex number in polar form
 $r\left(\cos\theta+i\sin\theta\right)$  

• 4(cos 270 + i sin 270)

• 4 (cos 0 + i sin 0)

• 4 (cos 90 + i sin 90)

• 4 (cos 180 + i sin 180)