Beginning Algebra, 11th Edition

Simplify.

Subtract in the radicand.

Factor out 2.

Divide out the common factor.

Separate into

real and imaginary parts.

x= 1  Standard form

26

2

i

ab

c =

a

c

b

x=^2 c^ ;

2



i 26

2

x=

2 i 26

2

x=

2 A 2 i 26 B

2122

=i# 2 # 26 = 2 i 26

2 - 24 =i 224 =i# 24 # 26

x=

4  2 i 26

4

x=

4  2 - 24

4

x=

4  216 - 40

4

SECTION 9.4 Complex Numbers 579

NOW TRY
EXERCISE 6
Solve for
complex solutions.

3 t^2 = 2 t- 1

NOW TRY ANSWER

6. e
   1
   3
   
   22
   3
   if

Factor first.

Then divide out

the common

factor.

The solution set is if. NOW TRY

26

2

e 1 

Complete solution available
on the Video Resources on DVD

9.4 EXERCISES

Write each number as a multiple of i.See Example 1.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
         
         
         4. 
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   6. 
      
      
      
      7. 
         
         
         
         8. 
            
         
         
         
         
      
      
      
      
   
   
   
   

Add or subtract as indicated. See Example 2.

9. 
   
   
   
   10. 
       
       
       
       11. 
           
       
       
       
       
   
   
   
   


10. 
    
    
    
    13. 
        
        
        
        14. 
            
        
        
        
        
    
    
    
    


11. 
    
    
    
    16. 
        
    
    
    
    


12. 
    
    
    
    18. 
        
    
    
    
    

Find each product. See Example 3.

19. 
    
    
    
    20. 
        
        
        
        21. 
            
        
        
        
        
    
    
    
    


20. 
    
    
    
    23. 
        
        
        
        24. 
            
        
        
        
        
    
    
    
    


21. 
    
    
    
    26. 
        
        
        
        27. 
            
        
        
        
        
    
    
    
    


22. 
    
    
    
    29. 
        
        
        
        30. 
            
        
        
        
        
    
    
    
    

Write each quotient in standard form. See Example 4.

31. 
    
    
    
    32. 
        
        
        
        33. 
            
        
        
        
        
    
    
    
    


32. 
    
    
    
    35. 
        
        
        
        36. 
            
        
        
        
        
    
    
    
    
    
    
    • i
      1 + 2 i
    
    
    
    

i

4 - 3 i

13

3 + 2 i

40

2 + 6 i

1

1 +i

1

1 - i

110 + 6 i 218 - 4 i 2 13 + 6 i 213 - 6 i 2 111 - 2 i 2111 + 2 i 2

13 + 2 i 214 - i 2 19 - 2 i 213 +i 2 15 - 4 i 213 - 2 i 2

1 - 5 i 21 - i 2 2 i 14 - 3 i 2 7 i 17 - 4 i 2

12 i 21 i 2 13 i 21 i 2 1 - 6 i 21 - i 2

13 - 4 i 2 + 16 - i 2 - 13 + 2 i 2 15 + 8 i 2 - 14 + 2 i 2 + 13 - i 2

1 - 3 + 6 i 2 - 5 112 - 3 i 2 - 8

11 +i 2 - 13 - 2 i 2 4 i+ 1 - 6 - 2 i 2 - 3 i+ 1 - 8 + 6 i 2

12 + 8 i 2 + 13 - 5 i 2 14 + 5 i 2 + 17 - 2 i 2 18 - 3 i 2 - 12 + 6 i 2

2 - 18 2 - 50 2 - 125 2 - 98

2 - 9 2 - 36 2 - 20 2 - 27