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MATH1720HomeworkChapter8Section1

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply.
 -3  - i
a.
none of these
c.
complex, nonreal complex
b.
real, complex
d.
complex, pure imaginary
 

 2. 
Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply.
12
a.
real, complex
c.
complex, pure imaginary
b.
pure imaginary
d.
complex, nonreal complex
 

 3. 
Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply.
0
a.
pure imaginary
c.
real, complex
b.
complex, nonreal complex
d.
complex, pure imaginary
 

 4. 
Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply.
 5i
a.
real, complex
c.
real
b.
complex, nonreal complex
d.
complex, pure imaginary
 

 5. 
Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply.
mc005-1.jpg
a.
complex, pure imaginary
c.
complex, nonreal complex
b.
pure imaginary
d.
real, complex
 

 6. 
Write the number as the product of a real number and i.
mc006-1.jpg
a.
4mc006-2.jpg
c.
-imc006-3.jpg
b.
-4i
d.
4i
 

 7. 
Write the number as the product of a real number and i.
 mc007-1.jpg
a.
imc007-2.jpg
c.
mc007-4.jpg
b.
-imc007-3.jpg
d.
imc007-5.jpg
 

 8. 
Write the number as the product of a real number and i.
-mc008-1.jpg
a.
3mc008-2.jpg
c.
-3imc008-4.jpg
b.
3imc008-3.jpg
d.
-3mc008-5.jpg
 

 9. 
Solve the quadratic equation and express all nonreal complex solutions in terms of i.
mc009-1.jpg +  80 = 0
a.
{±4imc009-2.jpg}
c.
{±imc009-3.jpg}
b.
{±4i}
d.
{±20i}
 

 10. 
Solve the quadratic equation and express all nonreal complex solutions in terms of i.
 mc010-1.jpg -  4x +  40 = 0
a.
{ 8,  -4}
c.
{ 2 ±  6i}
b.
{ 4 ±  12i}
d.
{-2 ±  6i}
 

 11. 
Solve the quadratic equation and express all nonreal complex solutions in terms of i.
5x2  + 3x =  -3
a.
mc011-1.jpg
c.
mc011-3.jpg
b.
mc011-2.jpg
d.
mc011-4.jpg
 

 12. 
Solve the quadratic equation and express all nonreal complex solutions in terms of i.
 4mc012-1.jpg +  9 =  5x
a.
mc012-2.jpg
c.
mc012-4.jpg
b.
mc012-3.jpg
d.
mc012-5.jpg
 

 13. 
Solve the quadratic equation and express all nonreal complex solutions in terms of i.
mc013-1.jpg =  5x -  10
a.
mc013-2.jpg
c.
mc013-4.jpg
b.
mc013-3.jpg
d.
mc013-5.jpg
 

 14. 
Perform the indicated operations. Simplify the answer.
mc014-1.jpg · mc014-2.jpg
a.
10
c.
-mc014-4.jpg
b.
-mc014-3.jpgi
d.
10i
 

 15. 
Perform the indicated operations. Simplify the answer.
mc015-1.jpg
a.
5i
c.
-5i
b.
-5
d.
5
 

 16. 
Perform the indicated operations. Simplify the answer.
mc016-1.jpg
a.
imc016-2.jpg
c.
mc016-3.jpg
b.
2i
d.
mc016-4.jpg
 

 17. 
Perform the indicated operations. Simplify the answer.
mc017-1.jpg
a.
- mc017-2.jpg
c.
- mc017-4.jpg
b.
mc017-3.jpg
d.
mc017-5.jpg
 

 18. 
Perform the indicated operations. Simplify the answer.
mc018-1.jpg
a.
4i
c.
-4
b.
-4i
d.
4
 

 19. 
Perform the indicated operations. Simplify the answer.
mc019-1.jpg
a.
2 + imc019-2.jpg
c.
2 + imc019-4.jpg
b.
2 - imc019-3.jpg
d.
2 - imc019-5.jpg
 

 20. 
Find the quotient. Write the answer in standard form.
 mc020-1.jpg
a.
- mc020-2.jpg + mc020-3.jpgi
c.
mc020-6.jpg + mc020-7.jpgi
b.
mc020-4.jpg + mc020-5.jpgi
d.
- mc020-8.jpg + mc020-9.jpgi
 

 21. 
Find the quotient. Write the answer in standard form.
 mc021-1.jpg
a.
- mc021-2.jpg - mc021-3.jpgi
c.
mc021-5.jpg - mc021-6.jpgi
b.
- mc021-4.jpgi
d.
mc021-7.jpg - mc021-8.jpgi
 

 22. 
Find the quotient. Write the answer in standard form.
mc022-1.jpg
a.
- mc022-2.jpg - mc022-3.jpgi
c.
mc022-6.jpg - mc022-7.jpgi
b.
- mc022-4.jpg - mc022-5.jpgi
d.
mc022-8.jpg - mc022-9.jpgi
 

 23. 
Find the quotient. Write the answer in standard form.
mc023-1.jpg
a.
mc023-2.jpg + mc023-3.jpgi
c.
mc023-6.jpg + mc023-7.jpgi
b.
mc023-4.jpg + mc023-5.jpgi
d.
mc023-8.jpg - mc023-9.jpgi
 

 24. 
Find the quotient. Write the answer in standard form.
mc024-1.jpg
a.
7i
c.
-7i
b.
7
d.
-7
 

 25. 
Perform the indicated operation. Write the result in standard form.
 ( 2  - 2i) + ( 6  + 8i)
a.
-4  + 10i
c.
-8  - 6i
b.
8  - 6i
d.
8  + 6i
 

 26. 
Perform the indicated operation. Write the result in standard form.
 ( 7 -  5i) + ( 4 -  2i)
a.
11 +  7i
c.
11 -  7i
b.
-11 -  7i
d.
11 -  3i
 

 27. 
Perform the indicated operation. Write the result in standard form.
 ( -9 +  15i) - ( 5 -  3i)
a.
-4 -  18i
c.
4 -  18i
b.
-14 -  18i
d.
-14 +  18i
 

 28. 
Perform the indicated operation. Write the result in standard form.
 ( -4  + 6i)  - 5
a.
1  - 6i
c.
1  + 6i
b.
9  - 6i
d.
-9  + 6i
 

 29. 
Perform the indicated operation. Write the result in standard form.
 ( 9  + 8i) - ( -8  - 8i) - ( -4  - 2i)
a.
21  + 18i
c.
13  + 14i
b.
21  - 2i
d.
-3  - 2i
 

 30. 
Find the product. Write the answer in standard form.
5i( 6  - 5i)
a.
30i  + 25i2
c.
25 + 30i
b.
- 30i  - 25i2
d.
30i - 25
 

 31. 
Find the product. Write the answer in standard form.
 ( 3  - 7i)( 2  - 5i)
a.
-29 + 29i
c.
-29 - 29i
b.
41 + 1i
d.
35i2  - 29i  + 6
 

 32. 
Find the product. Write the answer in standard form.
mc032-1.jpg
a.
61  + 60i
c.
11  + 60i
b.
11  - 60i
d.
61  - 60i
 

 33. 
Find the product. Write the answer in standard form.
 ( -3  + 6i)( -3  - 6i)
a.
9  + 36i2
c.
-27
b.
45
d.
9  - 36i2
 

 34. 
Find the product. Write the answer in standard form.
 (mc034-1.jpg  + 6i)(mc034-2.jpg  - 6i)
a.
-3
c.
39
b.
3  - 36i
d.
3  + 36i
 

 35. 
Simplify the power of i.
 mc035-1.jpg
a.
-1
c.
-i
b.
i
d.
1
 

 36. 
Simplify the power of i.
 mc036-1.jpg
a.
-i
c.
1
b.
i
d.
-1
 

 37. 
Simplify the power of i.
 mc037-1.jpg
a.
i
c.
-1
b.
1
d.
-i
 

 38. 
Simplify the power of i.
 mc038-1.jpg
a.
i
c.
1
b.
-i
d.
-1
 

 39. 
Simplify the power of i.
mc039-1.jpg
a.
-i
c.
i
b.
1
d.
-1
 

 40. 
In work with alternating current, complex numbers are used to describe current I, voltage E, and impedance Z. These three quantities are related by the equation E = IZ. Solve the equation E = IZ for the missing variable.
I = 7 + 2i, Z = 5 + 4i
a.
E = 35 + 46i
c.
E = 35 + 8i
b.
E = 43 + 38i
d.
E = 27 + 38i
 

 41. 
In work with alternating current, complex numbers are used to describe current I, voltage E, and impedance Z. These three quantities are related by the equation E = IZ. Solve the equation E = IZ for the missing variable.
 I = 6 + 5i, E = 30 + 44i
a.
Z = - mc041-1.jpg + mc041-2.jpg i
c.
Z = mc041-5.jpg + mc041-6.jpg i
b.
Z = mc041-3.jpg - mc041-4.jpg i
d.
Z = mc041-7.jpg + mc041-8.jpg i
 

 42. 
Indicate whether the statement is true always, sometimes, or never.
A real number is a complex number.
a.
Always
c.
Never
b.
Sometimes
 

 43. 
Indicate whether the statement is true always, sometimes, or never.
The sum of two imaginary numbers is an imaginary number.
a.
Always
c.
Never
b.
Sometimes
 

 44. 
Indicate whether the statement is true always, sometimes, or never.
The product of two imaginary numbers is a real number.
a.
Always
c.
Never
b.
Sometimes
 

 45. 
Indicate whether the statement is true always, sometimes, or never.
The product of a pair of complex conjugates (with b ? 0) is the difference of the squares of the real and imaginary parts.
a.
Always
c.
Never
b.
Sometimes
 

 46. 
Indicate whether the statement is true always, sometimes, or never.
When i is raised to an even power, the result is -1.
a.
Always
c.
Never
b.
Sometimes
 



 
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