hi there

how would i find all thew roots of a polynomial like this

z^4+z^3+(1-j)z+(j-1)=0

i have looked all over but cant find another example that includes anything like the (1-j)z term

thankyou

Printable View

- November 7th 2008, 08:34 AMphilyc86roots of complex numbers
hi there

how would i find all thew roots of a polynomial like this

z^4+z^3+(1-j)z+(j-1)=0

i have looked all over but cant find another example that includes anything like the (1-j)z term

thankyou - November 7th 2008, 02:01 PMmr fantastic
- November 7th 2008, 03:31 PMshawsend
How about doing it the old-school way:

(1) first convert it to the reduced quartic:

via a change of variable . Doing this I get:

Substituting this into the resolvent cubic:

yields:

This can now be solved as a cubic using the old-school approach to cubics. Make all the back substitutions to arrive at the roots. Lotta' work. Maybe an easier way though. - November 7th 2008, 03:34 PMmr fantastic
- November 7th 2008, 03:38 PMshawsend
I did solve it in Mathematica. The symbolic (exact) roots are very messy, too long for a single one to fit in the space allowed by Latex here.

- November 7th 2008, 03:40 PMshawsend
- November 7th 2008, 03:50 PMmr fantastic
- November 9th 2008, 03:27 AMphilyc86
hi

thanks for your replies .I did make a typo ,but only with the powers of the z terms ,which are 5 then 4 ,rather than 4 and 3 .any more ideas ? - November 9th 2008, 03:46 AMmr fantastic