math

find the trigonometric form of the complex number - (square root) 3 + i

  1. 👍 0
  2. 👎 0
  3. 👁 42
asked by laura
  1. let z = √3 + i
    magnitude = √(√3^2 + 1) = 2
    angle Ø:
    tanØ = 1/√3
    Ø = π/6 or 30°

    so z = 2(cos30° + i sin30°) or 2cis 30°
    or 2 cis π/6

    √z = z^(1/2)
    = √2( cos 15° + i sin15°) or √2(cos π/12 + i sin π/12)
    or √2 cis π/12

    for the nth root of a complex number, there will be n such solutions, so for the square root we need 2 answers
    2π/2 = π OR 360°/2 = 180°
    so by adding π radians or 180° to the appropriate form we get our second solution.

    so √z = √2cos15° + √2sin15° or √2cos195° + √2sin195°
    or
    √z = √2cos π/12 + √2sin π/12 or √2cos 13π/12 + i sin 13π/12

    in short form:
    √z = √2cis π/12 , √2cis 13π/12

    1. 👍 0
    2. 👎 0
    posted by Reiny
  2. just noticed the - sign in front of √3
    so our z = -√3 + i

    no big deal:
    the magnitude stays the same,
    however, the angle would now be in quad II
    so Ø = 150° or 5π/6

    making our
    √z = √2(cos 75° + i sin75°) OR √2( cos 5π/12 + i sin 5π/12)

    I will let you make these and the other changes for the second square root.

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. precal 2

    Reprenesent the complex number 5/2(square root of 3-i) graphically and find its trigonometric form.

    asked by danielle on July 29, 2011
  2. Math

    i^6 = (i^2)^3 = (-1)^3 = -1 The square, not the square root of -1 is 1. :) B.t.w., can you prove that -1 times -1 is 1? Hint, try to prove first that for any number X: -1 times X equals -X How do you find the square root of -1?

    asked by Count Iblis on November 15, 2006
  3. trigonometry

    find the polar form of the complex number: square root 3 minus square root 3i

    asked by Anonymous on April 28, 2011
  4. Math PLEASE HELP ASAP

    -PLEASE INCLUDE SOLUTIONS AND EXPLAIN HOW YOU DID IT PLEASE. *CHALLENGE. 1.SIMPLIFY : SQUARE ROOT OF 16^8+8^4/16^2+16^7 2.EXPRESS 1 + 1/1+SQUARE ROOT OF 2 - 1/1-SQUARE ROOT OF 2 IN THE FORM A+B SQUARE ROOT OF 2, WHERE A AND BARE

    asked by Aliza on December 10, 2012
  5. algebra

    1)Write the expression 9n^6+7n^3-6 in quadratic form,if possible A.9(n^3)^3+7n^3-6 B.9(n^2)^3+7(n^2)-6 C.9(n^3)^2+7(n^3)-6 D.not possible I'm thinking C on this one but im not sure 2)solve b^4+2b^2-24=0 A.-2,-square root of

    asked by Marissa on August 18, 2007
  6. algebra

    could someone please check these roblems for me and if they are not rightWOULD YOU PLEASE HELP E WITH THE CORRECT ONES THANKS!!! 1. Slove for X, wher X is the real number, square root 5x + 9= square root 9x + 13= 27 2. Find the

    asked by lee on October 31, 2010
  7. Algebra

    Hello Reiny, please check these problems for me and if they are not right WOULD YOU PLEASE HELP ME WITH THE CORRECT ONES THANKS!!! 1. Slove for X, wher X is the real number, square root 5x + 9= square root 9x + 13= 27 2. Find the

    asked by lee on October 31, 2010
  8. algebra

    1.)correct 2.)wrong---> the first term is wrong 4(3a^2)^2 = 36a^4 3.) not sure on this one 4.) wrong---> - square root of six is not a solution Hope this Helps! 1)find p(-3)if p(x)=4x^3-5x^2+7x-10 =-184 2)If r(x)=4x^2-3x+7,find

    asked by manny on August 16, 2007
  9. Math Answer Check

    P is a point on the terminal side of θ in standard position. Find the exact value of the six trigonometric functions for θ. P(-8, -8) Ans: cotangent: 1 secant: negative square root 2 cosecant: negative square root 2 sin: square

    asked by Anonymous on March 18, 2015
  10. College Algebra

    I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth

    asked by Krissy on January 19, 2013

More Similar Questions