equation complex number

z^4 + 81 = 0 (solve)

change it to polar, then take the root.

z^4= 81@180
z= 3@180/4 + n90 where n=0, 1, 2, 3

check:
z= 3@180/4 + 3*90=3@315
z^4=81@(4*315)=81@1260= 91@180=-81
you can check it at the other roots also.

this is what i did:

z^4 = - 81
z (81 cis 180)^1/4
81 ^ 1/4 cis 1/4 * 180
3 cis 45 therefore 360/4 = 90*
4 solutions:
3 cis 45*
3 cis 135*
3 cis - 135*
3 cis - 45*
???

That is it. You get four roots, the same as mine. I did not use positive and negative angles, just positive. That is a preference I have. It is easier for me to think of rotation in one direct, so your -45 is 315 for me.

thanks for the help, a bit confusing trying to read explanations for maths over the internet but hey we got the right answers. :)

It does take a while to understand the ASCII labels for math. Fractions are the most difficult..

  1. 👍 0
  2. 👎 0
  3. 👁 381
asked by kevin

Respond to this Question

First Name

Your Response

Similar Questions

  1. Trigonometry

    Given the rectangular-form point (–1, 4), which of the following is an approximate primary representation in polar form? A. −(4.12, 1.82) B. (−4.12, −1.33) C. (4.12, 1.82) D. (4.12, 4.96) Change 8 cis 240degrees to

    asked by Anonymous on August 7, 2012
  2. Pre-calculus- URGENT

    Convert the rectangular coordinate (-8,i (square root of 3) into polar coordinates. How do I do this?? I tried every way I knew of to convert the y coordinate (i (square root of three)) to polar form, but it didn't work. I think

    asked by Ellie on September 13, 2015
  3. chemistry

    Determine if it is polar or non-polar molecule: C3H6O C2H5OH SiCl4 NH3 CO2 C3H8 H2O N2 My ans are: Polar Polar Polar polar Nonpolar nonpolar polar Nonpolar are my answers correct???? No one has answered this question yet.

    asked by nadira on March 5, 2013
  4. CHEMISTRY

    Determine if it is polar or non-polar molecule: C3H6O C2H5OH SiCl4 NH3 CO2 C3H8 H2O N2 My ans are: Polar Polar Polar polar Nonpolar nonpolar polar Nonpolar are my answers correct????

    asked by nidscorection on March 5, 2013
  5. bio (plasma membrane)

    I understand that the plasma membrane is composed of a polar head and non polar tail. I read in my textbook that small non-polar molecules readily pass through and that polar and non-polar repel. so how do non-polar substance pass

    asked by lou on February 19, 2011
  6. CHEMISTRY

    Determine if it is polar or non-polar molecule: C3H6O C2H5OH SiCl4 NH3 CO2 C3H8 H2O N2 My ans are: Polar Polar Polar Nonpolar polar Nonpolar are my answers correct????

    asked by nidscorection on March 5, 2013
  7. Algebra

    I had to solve the function g of f where f is x^2+1 and g is sq. root of x. I wrote this out as the sq. root of x^2+1. The ^2 and the sq. root canceled each other out, so I was left with x + sq. root of 1. But my book got sq. root

    asked by Adriana on October 28, 2009
  8. Chem

    Is a C-H bond polar or non-polar? Is a C-Cl bond polar or non-polar? I have different sources giving me different ranges. One says that anything with an electronegetivity of 0.5 or less is non-polar and I have anothre source

    asked by Lena on July 8, 2009
  9. Algebra

    Solve 2+ the square root of 4-x=x what is your question? ok lets start by arranging everything so its easier to solve.. u want to put the square root(4-x)on one side of the equation and the 2 on the other side... square root(4-x)

    asked by Joy on August 15, 2007
  10. Pre Algebra

    Please help me with some problems. Thank you! Solve the equation by square root property. 3. 2x^2 = 26 I don't understand how to solve this problem. Solve the equation using the quadratic formula. 7. 7x^2=-8x -2 This is what I got

    asked by Nikki on August 18, 2007
  11. Algebra

    I had to solve 2x^2-x-1 using the quad. formula. I got it down to (1 +/- the square root of neg. 8) divided by four. I broke the sq. of neg. 8 into the sq. root of 4 and the sq. root of -2. But my question is could it also be the

    asked by Corinna on October 10, 2009

More Similar Questions