Math

Find all solutions for the complex numbers:

a) z^4 = 9i -46
b) 8*sqrt3 / z^4 +8 =+i

  1. 👍 0
  2. 👎 0
  3. 👁 54
  1. best convert to polar form

    z^4 = 46.87 cis 2.95
    so, z = 2.62 cis 0.738 + k*pi/2 for k=0..3
    then convert back to rectangular form.

    1. 👍 0
    2. 👎 0
    posted by Steve
  2. using de Moivre's Theorem:

    let z^4 = -46 + 9i

    changing -46 + 9i to rectangular form
    r = √46^2+9^2 =√2197
    tanØ = 9/-46
    Ø = 168.9298°

    z^4 = √2197(cos168.9298° + i sin 168.9298°)
    z = .....
    so there will be 4 roots,

    z = √2197^(1/4) (cos (168.9.. +k(360°)/4 + i sin(168.9..+k(360°)/4 )
    where k = 0, 1, 2, 3

    if k = 0

    z = √2197^(1/4) (cos42.2324 + i sin42.2324)
    = 2.61655(.740424 , .67214 i )
    = (1.937355 , 1.758687 i )

    if k = 1
    z = √2197(1/4) (cos 132.2324° + i sin 132.2324°)
    = ( -1.758687 , 1.937355 i)

    k = 2
    I will let you finish the other two.

    testing for k = 1

    if z = ( -1.758687 , 1.937355 i)
    r = appr 2.61655
    Ø = 132.2324
    then z^4 = 2.6155^4 (cos 4(132.2324) , i sin 4(132.2324))
    = 46.872...(-.98139.. , .19201..)
    = -46 + 9i , YEAAAAHHH

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    Find a polynomial function of degree 3 with the given numbers as zeros. -5, sqrt3, -sqrt3 Would this work as a function for this problem? Please help. Thanks! f(x) =(x-r1) (x-r2) (x-r3) =(x-(-5)) (x-sqrt3) (x--sqrt3) (x+5))

    asked by Alyssa on July 22, 2009
  2. Algebra

    Find the exact solution(s) of the system: x^2/4-y^2=1 and x=y^2+1 A)(4,sqrt3),(4,-sqrt3),(-4,sqrt3),(-4,-sqrt3) B)(4,sqrt3),(-4,sqrt3) C)(2,1),(2,-1),(4,sqrt3),(4,-sqrt3) D)(4,sqrt3),(4,-sqrt3) I don't know

    asked by Jon on February 21, 2008
  3. Math

    Find the exact solution(s) of the system: x^2/4-y^2=1 and x=y^2+1 A)(4,sqrt3),(4,-sqrt3),(-4,sqrt3),(-4,-sqrt3) B)(4,sqrt3),(-4,sqrt3) C)(2,1),(2,-1),(4,sqrt3),(4,-sqrt3) D)(4,sqrt3),(4,-sqrt3)

    asked by Jon on February 21, 2008
  4. Algebra

    Rationalize denominator, all variables positive real numbers and denominator is not zero. sqrt3/3 sqrt2 - sqrt3 sqrt3(3sqrt2+sqrt3)/18-3 3 sqrt6+3/18-3 3 sqrt 6+3/15 (is this my answer)

    asked by Lori on March 13, 2008
  5. Algebra

    Find a polynomial function of degree 3 with the given numbers as zeros. -5, sqrt3, -sqrt3

    asked by Breanna on July 14, 2009
  6. Algebra

    Find a polynomial function of degree 3 with the given numbers as zeros. -5, sqrt3, -sqrt3

    asked by Beth on July 21, 2009
  7. Calculus

    Find any absolute maximum and minimum and local maximum and minimum for the function f(x)=x^3-4x+5 on the interval [0,5). Make sure to prove that these points are max/min values. THis is what I did. f'(x)=3x^2-4=0 x= +/- 2/sqrt3

    asked by Janet on April 17, 2011
  8. Calculus

    Find the equation (in terms of x and y) of the tangent line to the curve r=3sin3(theta) at theta=pi/4. I don't know if I'm taking the right approach for this question but her goes what I did: I found the slope I got

    asked by Jessica on October 13, 2011
  9. Math

    Given that an equation of the form f(x) = x^n has n solutions, and that the solutions are equally spaced at a given radius in the complex plane, discuss why complex solutions must occur in conjugate pairs when .

    asked by April on November 20, 2015
  10. Math

    Given that an equation of the form f(x) = x^n has n solutions, and that the solutions are equally spaced at a given radius in the complex plane, discuss why complex solutions must occur in conjugate pairs when .

    asked by April on November 17, 2015

More Similar Questions