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
Vadim26 [7]
2 years ago
8

Find the solution of the following equation whose argument is strictly between 270^\circ270 ∘ 270, degree and 360^\circ360 ∘ 360

, degree. Round your answer to the nearest thousandth. z^4=-625z 4 =−625
Mathematics
1 answer:
Natasha2012 [34]2 years ago
5 0

\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}]

\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}]

Argument of Complex number

Z=x+iy , is given by

If, x>0, y>0, Angle lies in first Quadrant.

If, x<0, y>0, Angle lies in Second Quadrant.

If, x<0, y<0, Angle lies in third Quadrant.

If, x>0, y<0, Angle lies in fourth Quadrant.

We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is

   \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]

You might be interested in
$1,000, 5%, 2 years of simple interest paid to the nearest cent
yawa3891 [41]
Using the formula for simple interest
(1000 X 5 X 2)/100
the answer is $100 but to the nearest cent it is 10000cents
7 0
3 years ago
You must use the Substitution method
elena-14-01-66 [18.8K]
3x+2y=5w is your answer so your main/real answer is 5w
3 0
3 years ago
A car travled 200 miles in 4 hours . What was the car average rate of speed in miles per hour ?
Dahasolnce [82]

rate = 200 miles/ 4 hours = 50 miles/hour

7 0
3 years ago
Read 2 more answers
Please help and fast for brainliest
faust18 [17]

Answer:

3 gallons

Step-by-step explanation:

For every value of green ( 'x') ....white is 3 times as much

  for 1 gallon green     ====> 3 gallons white

5 0
1 year ago
Let n be the number of couples dancing in a competition. If there are 5 organizers, which expression represents the total number
Korvikt [17]
2n+5...a couple is two people so you need to multiply the number of couples, n, by 2 to get the total number of dancers. Then add the total number of organizers.
3 0
3 years ago
Other questions:
  • You are 5 feet tall and cast a 10 foot shadow a flagpole nearby cast a shadow that is 28 feet which equation can you use to solv
    12·1 answer
  • Which equation supports the given conjecture?
    12·1 answer
  • Write the equation of a line that is parallel to y = -0.75x and that passes through the point (8,0).
    13·1 answer
  • Find the GCF of 72 and 81. Show your work. (3 points) Part C: Using the GCF you found in Part B, rewrite 72 + 81 as two facto
    10·1 answer
  • PLEASE HELP ME WITH THIS
    10·2 answers
  • For all values of x, f(x) = x^2 + 1 and g(x) = x-5
    11·1 answer
  • Help me with this please
    12·1 answer
  • 225125 in base 6 divided by 101 in base 6<br>​
    6·1 answer
  • Solve please I need help 3x+6=-2
    8·2 answers
  • In an examination, 40% of students passed in Maths only, 30% passed in Science only and 10% students failed in both subjects. If
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!