1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tatyana61 [14]
3 years ago
10

Which expression is a cube root of -1+i sqrt3

Mathematics
1 answer:
Marina CMI [18]3 years ago
4 0
If z=-1+i \sqrt{3}, then 

Rez=-1
Imz= \sqrt{3} and 
|z|= \sqrt{Re^2z+Im^2z}= \sqrt{1^2+ (\sqrt{3})^2 }= \sqrt{4}=2.
Then cos\theta = \frac{Rez}{|z|} = \frac{-1}{2}sin\theta = \frac{Imz}{|z|}= \frac{ \sqrt{3} }{2}.

Since \theta \in (-\pi,\pi], you can conclude that \theta= \frac{2\pi}{3}.
The triginometric form of z is z=|z|(cos\theta+isin\theta)=2(cos \frac{2\pi}{3} +isin \frac{2\pi}{3} ).
Use formula \sqrt[3]{z} =\{ \sqrt[3]{|z|} (cos \frac{\theta+2\pi 
k}{n}+isin \frac{\theta+2\pi k}{n} ), k=0,1,2\} to find cube root. 
For k=0, z_1= \sqrt[3]{2} (cos \frac{ 
\frac{2\pi}{3} }{3} +isin\frac{ \frac{2\pi}{3} }{3})= \sqrt[3]{2} (cos 
40^0+isin 40^0),
For k=1, z_1= \sqrt[3]{2} (cos
 \frac{ \frac{2\pi}{3}+2\pi }{3} +isin\frac{ \frac{2\pi}{3}+2\pi }{3})= 
\sqrt[3]{2} (cos 160^0+isin 160^0),
For k=2, z_1= \sqrt[3]{2} (cos \frac{ \frac{2\pi}{3}+4\pi }{3} +isin\frac{ 
\frac{2\pi}{3}+4\pi }{3})= \sqrt[3]{2} (cos 280^0+isin 280^0).
Answer: The correct choice is C.
You might be interested in
Edward buys a bicycle online for 254.75$ if shipping and handling are an additional 24% of the price how much shipping and handi
balu736 [363]

Answer:

24% of (254.75 US$) =

61.14 US$

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Robert had $300 in the bank yesterday. Then, Robert bought a sofa for $500, but didn't realize that he overdrew from his bank. H
strojnjashka [21]

Answer:-200

Step-by-step explanation:

300-500=-200

3 0
2 years ago
Find the solution to the system of equations,
olya-2409 [2.1K]
A is the answer :)
Since we are given z = 8, finding y is simple.
By replacing the z in y + z = 11, we can see that y = 3
After finding these two, x can be found
5 0
2 years ago
Read 2 more answers
Multiple choice please please answer
lakkis [162]

Answer:

\purple { \boxed{x = 25 \times  \sin \: 39 \degree}}

Step-by-step explanation:

\sin \: 39 \degree =  \frac{x}{25}  \\ 25 \times  \sin \: 39 \degree = x \\  \huge \red{ \boxed{x = 25 \times  \sin \: 39 \degree}}

4 0
3 years ago
Y =3x+2 is the equation of a straight line graph.where does it cross the y-axis
neonofarm [45]
Cross the y-axis in x=0
therfore:
if x=0; y=3*0+2=2; ⇒ P(0,2)

solution: P(0,2).
7 0
3 years ago
Other questions:
  • A minute-hand is 16 in long. Find the distance traveled by the tip of the minute-hand in one hour.
    6·2 answers
  • Graph the function f(x)=4x^2
    10·2 answers
  • What is 3 7/10 times 7
    5·1 answer
  • How can you get the square side area??
    8·1 answer
  • Fred bought 1.75 liters more laundry detergent than bleach (True or False)
    9·1 answer
  • Question 7: What is the probability of drawing the complement of a king or a queen from a standard deck of
    12·1 answer
  • What is the equation in point-slope form of the line passing through (3, 6) and (−2, 1)?
    5·1 answer
  • What does x equal -4 = x - 93/-1
    15·1 answer
  • A football team scored 3 touchdowns, 3 extra points, and 4 field goals.
    11·2 answers
  • A circular garden with an inner diameter of 8 meters is surrounded by a walkway of width 2 meters. Find the area of the walkway
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!