Roots & Imaginary Roots
I have got a few questions about equations involving imaginary roots.
First, how can I graphically represent the imaginary root?(We can use formulas for quadratic equations but how to do it with 3rd , 5th etc. degree equations?)
Second, does a Nth degree equation have n roots or its graphic has n number of curves?
Last one, is there any formula derived to find the roots of an equation involving variables at least raise to their 3rd power?
I do not know much LaTeX so I can not write the equations , if you do not understand anything please do not hesitate to ask.
Originally Posted by JohnDoe
You need to look at the complex plain to find the n roots on a graph, googling complex plain will do better than me trying to explain it
the nth degree equation does have n roots in the complex numbers (fundamental theorem of algebra)
there is a formula to polynomials of degree 1,2,3,4 beyond that the equations aren't solvable via roots
The Cubic Formula
Thanks for reply but isn't the complex plane same as the x-y plane we draw the function on?
yeah I mean the x axis becomes the real axis and the y axis becomes the imaginary axis, but you cannot draw like y=x^5 where x is a real number on the complex plane, becomes the outputs are real numbers and not imaginary numbers, you have to create special cases and interpret special things to draw on the complex plane,
for example, interpreting a+bi as a vector and plotting it on the complex plane is fine, but lets say you want to graph the equation f(z)=z^3, where z is complex,
This function takes as inputs a complex number, which can be represented as (a,b) with a and b real numbers, and spits out another complex number, so you're in 4 dimensions, which you cannot plot on a 2d axis
Thanks for reply BTW to fully understand can you show any graphical proof or give links about this topic?