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
ra1l [238]
3 years ago
8

If

"absmiddle" class="latex-formula"> and z^{6}=a+bi, then a = _ and b = _
Mathematics
1 answer:
Luden [163]3 years ago
3 0

Rewriting z in polar form makes this trivial.

z=|z|e^{i\mathrm{arg}(z)}

We have

|z|=\sqrt{(-1)^2+(-\sqrt3)^2}=2

\mathrm{arg}(z)=\tan^{-1}(-1,-\sqrt3)=-\dfrac{2\pi}3

(not to be confused with the standard inverse tangent function \tan^{-1}x. Here \tan^{-1}(x,y) is the inverse tangent function that takes into account position in the coordinate plane; look up "atan2" for more information)

So we have

z=-1-\sqrt3\,i=2e^{-2\pi/3\,i}

Then

z^6=2^6\left(e^{-2\pi/3\,i}\right)^6=64e^{-4\pi\,i}=64

so that a=64 and b=0.

You might be interested in
What is the sum of 1 1/2 and 2/3
prisoha [69]

1\dfrac{1}{2}+\dfrac{2}{3}=1+\dfrac{1\cdot3}{2\cdot3}+\dfrac{2\cdot2}{3\cdot2}=1+\dfrac{3}{6}+\dfrac{4}{6}=1+\dfrac{3+4}{6}=1+\dfrac{7}{6}=1+1\dfrac{1}{6}=2\dfrac{1}{6}\\\\Answer:\ \boxed{1\dfrac{1}{2}+\dfrac{2}{3}=2\dfrac{1}{6}}

6 0
3 years ago
Read 2 more answers
Help please and don't delete the question
Ahat [919]

Answer:

x = 2

Step-by-step explanation:

8(4-x) = 7x + 2

1) Distribute : 32 - 8x = 7x + 2

2) Subtract 32 : -8x = 7x - 30

3) Subtract 7x : -15x = -30

4) Divide 15 : x = 2 :)

4 0
3 years ago
Read 2 more answers
The lengths of three sides of a triangle are 2x, 3x-4, and x+4. Find a value of x that makes the triangle equilateral
Furkat [3]
Espero que no me jusgas por esto que estoy escribiendo
4 0
3 years ago
frederick is designing a poster that has 3-in borders on the top and bottom and 2-in borders on the left and right sides. they a
kiruha [24]

Answer:

idk

Step-by-step explanation:

idk

4 0
3 years ago
Find the total cost if a pair of shoes cost $49.95 and the tax is 5.5%
serious [3.7K]

Answer:

52.70

Step-by-step explanation:

49.95x.055=2.75 tax

49.95+2.75=52.70 total costs

7 0
3 years ago
Other questions:
  • A chef can make 12 omelets in one hour. What is the rate of omelets per minute?
    8·1 answer
  • Sandra normally takes 2 hours to drive from her house to her grandparents' house driving her usual speed. However, on one partic
    10·1 answer
  • PLZ HELP ASAP. What is the measure of B?
    5·2 answers
  • Determine the volume of the solid that lies between planes perpendicular to the x-axis at x=0 and x=4. The cross sections perpen
    6·1 answer
  • What’s the correct solution to 2x^2+8x=x^2-16
    8·1 answer
  • Auto insurance can be purchased to cover which of the following liabilities? a. bodily injury b. property damage c. both a &
    5·1 answer
  • A silk ribbon costs $5.60 for 0.8m. How much does 3.25m of this silk ribbon cost?
    9·2 answers
  • I don’t get how to solve this
    9·1 answer
  • My parents recently moved to the Poconos, they got 30 or more inches of
    12·1 answer
  • Which number is an integer?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!