1a) (5, 435o) I added 360o
1a) (-5, 255o) I added 180o


1b) (4, 11p/4) I added 2p
1b) (-4, 7p/4) I added p


               _____
2a) r = \/ 9 + 16 = 5 and tan (4/3) = 53.1o This is the reference angle. The angle is supposed to be in the 2nd quadrant. Subtract from 180.
Answer is   (5, 126.9o)


2b) Easy one. r = 4 and q = 180o  Why?
Answer is: (4, 180o)


             _______
3) r = \/ 25 + 169 = 13.9 and Tan(13/5) = 1.21 in rads.
Answer is: (13.9, 1.21) 


4a) x = 7cos 240o = -3.5 and y = 7sin 240o = -6.1
Answer is: (-3.5, -6.1) 


4b) x = 3cos 142o = -2.4 and y = 3sin 142o = 1.8
Answer is: (-2.4, 1.8) 

5a) 
5b)           5c) 
5d)      5e) 
5f)            5g) 

6) r = 3.6 and 0 = 33.7o
Answer is: 3.6cis 33.7o       


7) a = 5cos 320o and b = 5 sin 320o
Answer is: 3.8 - 3.2i      


8) z1 = 5.8cis 59o and z2 = 7.8cis 50.2o
a) z1z2 = 45.2cis 109.2o
b) a = 45.2cos109.2o and b = 45.2sin 109.2o
Answer is: -14.9 + 42.7i       


9) 9cis 120o


10a) z = 1.4cis 45o and z6 = (1.4)6 cis (6)(45o) = 7.5 cis 270o
b) a = 7.5cos 270o and b = 7.5sin 270o
Answer is:  -7.5i       


11) The three cubed roots of one are found as follows:
for k = 0,      = 1cis 120o = -1/2 + .87i
for k = 1       = 1cis 240o = -1/2 - .87i
for k = 2       = 1cis 360o = 1       

 
 
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 Chapter 13
 
 
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