math.answers.com/math-and-arithmetic/How_do_you_find_three_cube_roots_of_-64

Preview meta tags from the math.answers.com website.

Linked Hostnames

8

Thumbnail

Search Engine Appearance

Google

https://math.answers.com/math-and-arithmetic/How_do_you_find_three_cube_roots_of_-64

How do you find three cube roots of -64? - Answers

Not calculus, but -64 has three cube roots, two of which are complex numbers. Note, sqrt(-1) = i. 4*e^(pi*i/3) is a root because [4*e^(pi*i/3)]^3 = 64*e^(pi*i) = 64*-1= -64 4*e^(-pi*i/3) is a root because [4*e^(-pi*i/3)]^3 = 64*e^(-pi*i) = 64*-1= -64 and of course -4 = 4*e^(pi*i) is a root because (-4)^3 = -64. To find these, set up the equation -64 = [A*e^(pi*i*B)]^3 and solve for A and B. If you don't like using complex exponentials, any complex number can also be written as a + b*i so you could solve -64 = (a + bi)^3. If you use the complex exponential form, you should get the three answers above. If you use the a + b*i form you should get the equivalent {2 +/- 3.464i, -4}. Remember either equations has three solutions because it is cubic.



Bing

How do you find three cube roots of -64? - Answers

https://math.answers.com/math-and-arithmetic/How_do_you_find_three_cube_roots_of_-64

Not calculus, but -64 has three cube roots, two of which are complex numbers. Note, sqrt(-1) = i. 4*e^(pi*i/3) is a root because [4*e^(pi*i/3)]^3 = 64*e^(pi*i) = 64*-1= -64 4*e^(-pi*i/3) is a root because [4*e^(-pi*i/3)]^3 = 64*e^(-pi*i) = 64*-1= -64 and of course -4 = 4*e^(pi*i) is a root because (-4)^3 = -64. To find these, set up the equation -64 = [A*e^(pi*i*B)]^3 and solve for A and B. If you don't like using complex exponentials, any complex number can also be written as a + b*i so you could solve -64 = (a + bi)^3. If you use the complex exponential form, you should get the three answers above. If you use the a + b*i form you should get the equivalent {2 +/- 3.464i, -4}. Remember either equations has three solutions because it is cubic.



DuckDuckGo

https://math.answers.com/math-and-arithmetic/How_do_you_find_three_cube_roots_of_-64

How do you find three cube roots of -64? - Answers

Not calculus, but -64 has three cube roots, two of which are complex numbers. Note, sqrt(-1) = i. 4*e^(pi*i/3) is a root because [4*e^(pi*i/3)]^3 = 64*e^(pi*i) = 64*-1= -64 4*e^(-pi*i/3) is a root because [4*e^(-pi*i/3)]^3 = 64*e^(-pi*i) = 64*-1= -64 and of course -4 = 4*e^(pi*i) is a root because (-4)^3 = -64. To find these, set up the equation -64 = [A*e^(pi*i*B)]^3 and solve for A and B. If you don't like using complex exponentials, any complex number can also be written as a + b*i so you could solve -64 = (a + bi)^3. If you use the complex exponential form, you should get the three answers above. If you use the a + b*i form you should get the equivalent {2 +/- 3.464i, -4}. Remember either equations has three solutions because it is cubic.

  • General Meta Tags

    22
    • title
      How do you find three cube roots of -64? - Answers
    • charset
      utf-8
    • Content-Type
      text/html; charset=utf-8
    • viewport
      minimum-scale=1, initial-scale=1, width=device-width, shrink-to-fit=no
    • X-UA-Compatible
      IE=edge,chrome=1
  • Open Graph Meta Tags

    7
    • og:image
      https://st.answers.com/html_test_assets/Answers_Blue.jpeg
    • og:image:width
      900
    • og:image:height
      900
    • og:site_name
      Answers
    • og:description
      Not calculus, but -64 has three cube roots, two of which are complex numbers. Note, sqrt(-1) = i. 4*e^(pi*i/3) is a root because [4*e^(pi*i/3)]^3 = 64*e^(pi*i) = 64*-1= -64 4*e^(-pi*i/3) is a root because [4*e^(-pi*i/3)]^3 = 64*e^(-pi*i) = 64*-1= -64 and of course -4 = 4*e^(pi*i) is a root because (-4)^3 = -64. To find these, set up the equation -64 = [A*e^(pi*i*B)]^3 and solve for A and B. If you don't like using complex exponentials, any complex number can also be written as a + b*i so you could solve -64 = (a + bi)^3. If you use the complex exponential form, you should get the three answers above. If you use the a + b*i form you should get the equivalent {2 +/- 3.464i, -4}. Remember either equations has three solutions because it is cubic.
  • Twitter Meta Tags

    1
    • twitter:card
      summary_large_image
  • Link Tags

    16
    • alternate
      https://www.answers.com/feed.rss
    • apple-touch-icon
      /icons/180x180.png
    • canonical
      https://math.answers.com/math-and-arithmetic/How_do_you_find_three_cube_roots_of_-64
    • icon
      /favicon.svg
    • icon
      /icons/16x16.png

Links

59