Concepts in complex numbers

 $5cis\ \left(\frac{\pi}{3}\right)\ \times3cis\left(\frac{\pi}{6}\right)$  

•  $8cis\left(\frac{\pi}{2}\right)$  

•  $15cis\ \left(\frac{\pi}{2}\right)$  

•  $15cis\left(\frac{\pi}{6}\right)$  

•  $8cis\left(\frac{\pi}{6}\right)$  

When converting between rectangular and polar coordinates,

x = ?

 Write the complex number - 3i in polar form.

• 3 ( cos 3π/2 + i sin 3π/2)

• 9 ( cos 3π/2 + i sin 3π/2)

• 3 ( cos π/2 + i sin π/2)

• 3 ( cos 3π/2 - i sin 3π/2)

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

• (5,3)
• (20,12)
• (-20,-12)
• (-5,-3)

• -3

• 3 + i

• 9

 $z_1=9\angle160\degree\ ,\ z_2=3\angle75\degree$  find  $\frac{z_1}{z_2}$  in polar form

•  $3\angle85\degree$  

•  $0.3333\angle85\degree$  

•  $3\angle2.13\degree$  

•  $3\angle-85\degree$  

What is the radius to the following rectangular point:

(5, 2)

• 5

• 2

• √29

• √27

• Symmetric with respect to the polar axis

• Symmetric with respect to the origin

• No symmetry

When a point is rotated 360 degrees around the origin, what are the final coordinates if the initial coordinates were (0, 0)?

• (0, 1)

• (0, 0)

• (1, 0)

• (1, 1)