Answers  GP1-­‐PAP-­‐S1-­‐HW1  1.   −196 = 14𝑖  

2.  3 −18 = 9𝑖 2  

3.   −120 = 2𝑖 30  

4.   −80 = 4𝑖 5  

5.  𝑖!" = −1  

6.    𝑖!" = 1  

7.  𝑖!" = 𝑖  

8.  𝑖!" = −𝑖  

9.  𝑖!"! =  𝑖  

10.  𝑖!"# = 1  

11.   5− 3𝑖 + −7+ 2𝑖 = −2− 𝑖  

12.  7− 2− 5𝑖 + 9𝑖 = 5+ 14𝑖  

13.   −41+ 12𝑖 − 17− 25𝑖 + 30− 10𝑖 = −28+ 27𝑖  

14.  −13− 9𝑖 + 6𝑖 − 11+ 7𝑖 + 10 = −14− 10𝑖  

15.   3𝑖 − 19 + 22− 11𝑖 − 16+ 8𝑖 = −13− 16𝑖  

16.  −12𝑖 + 7− −5− 8𝑖 + 𝑖 − 1 = 11− 3𝑖      

GP1-­‐PAP-­‐S1-­‐HW2  1.   6+ 5𝑖 6− 5𝑖 = 61  

2.   −3+ 1𝑖 −3− 1𝑖 = 10  

3.   9− 2𝑖 9+ 2𝑖 = 85  

4.   1− 12𝑖 1+ 12𝑖 = 145  

5.    7𝑖(3− 4𝑖) = 28+ 21𝑖  

6.  𝑖 2− 3𝑖 + 8 1− 4𝑖 = 11− 30𝑖  

7.   6− 5𝑖 3+ 𝑖 = 23− 9𝑖      

8.  (11− 2𝑖)! = 117− 44𝑖  

9.  (3− 7𝑖)(4− 5𝑖) = −23− 43𝑖      

10.   2+ 𝑖 1− 𝑖 2+ 3𝑖 = 9+ 7𝑖  

11.    (2− 𝑖)! = 2− 11𝑖  

12.     4+ 3𝑖 2− 5𝑖 2+ 5𝑖 4− 3𝑖 = 725  

13.   6+ 𝑖 6− 𝑖 − (3+ 4𝑖)(4− 3𝑖) = 13− 7𝑖      

14.  2𝑖 5− 𝑖 + 3𝑖(7𝑖 − 2) = −19+ 4𝑖  

15.   1− 𝑖 5+ 𝑖 − 2𝑖(−3− 𝑖)  = 4+ 2𝑖  

16.   −8+ 5𝑖 𝑖 − 2 − (6+ 𝑖)(𝑖 − 3)  = 30− 21𝑖    

GP1-­‐PAP-­‐S1-­‐HW3  1.  !!!!

!!= 3− !

!𝑖  

2.  !!!"!!!!

= −4+ 3𝑖  

3.  !!!!!!!

= !!+ !

!𝑖      

4.  !"!!!!

= !"!+ !!

!𝑖  

5.    !!!!!!

= !!+ !!

!𝑖  

6.  !!!!!!!!

= !!!"+ !"

!"𝑖  

7.  !!!!!!!!

= !!"+ !"

!"𝑖  

8.  !!!!!!!!

= −𝑖  

9.  !!!!!!!

+ !!!!!!

= 6− 2𝑖  

10.  !!!!!!!!

− !!!!!!!

= !!"!"− !

!"𝑖  

11.  !!!!!!!!

+ !!!!!!!

= !!!!− !

!𝑖  

12.  !!!!!!!!!

− !!!!!!!!

= !!!𝑖  

GP1-­‐PAP-­‐S1-­‐HW4  1b.   2− 3𝑖 = 13  

2b.   −6𝑖 = 6  

3a.  7− 7𝑖  

4.  6𝑖  

5.   !"!!!!!!!

= 5  

6.   !"!!"!!!!"!

= 5  

7.   !!!!!!

− !!!!!!!

= 34  

8.   2+ 5𝑖 ! = −142− 65𝑖  

9.   !!!!! !

= !!"#!"#$%

+ !"!"#$%

𝑖  

Note:  24389 = 29!;      142 = 2 ∙ 71;        65 = 13 ∙ 5