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Complex roots

Total questions: 8

Worksheet time: 10mins

Name
Class
Date
1.

How many roots does the equation

z11 - 1 =0 have?

a)

10

b)

11

c)

1

d)

0

2.

How many real solutions are there to the equation z8 - 1 =0 ?

a)

0

b)

2

c)

1

d)

8

3.

How many real solutions are there to the equation z7 -1 =0 ?

a)

2

b)

0

c)

1

d)

7

4.

One root of z6 = - 8i 


 is

a)

1 + i

b)

1 - i

c)

2(1 + i)\sqrt{2}\left(1\ +\ i\right)

d)

2(1i)\sqrt{2}\left(1-i\right)

5.

If   ω\omega  is a complex cube root of 1, then the value of 

 1 +ω4+ω81\ +\omega^4+\omega^8  is

a)

0

b)

 ω\omega  

c)

 ω-\omega  

d)

 ω2\omega^2  

6.

Which of the following cannot be the argument of a complex number z, such that  z9 =1 + iz^{9\ }=-1\ +\ i   ?

a)

 11π36\frac{11\pi}{36}  

b)

 π12\frac{\pi}{12}  

c)

 29π36\frac{29\pi}{36}  

d)

 19π36\frac{19\pi}{36}  

7.

One of the following is a solution to
 (z + 1)4=16\left(z\ +\ 1\right)^4=-16  
Which one?

a)

 2+(21)i\sqrt{2}+\left(\sqrt{2}-1\right)i  

b)

 2+2i\sqrt{2}+\sqrt{2}i  

c)

 21+2i\sqrt{2}-1+\sqrt{2}i  

d)

 21+(21)i\sqrt{2}-1+\left(\sqrt{2}-1\right)i  

8.

Which of the diagrams below represents the set of complex numbers z such that  z3=iz^3=i ?

a)
b)
c)
d)
e)

None