The discussion revolves around solving the complex polynomial equation (z^4) + 1 = 0, focusing on the roots of the equation in the context of complex numbers.
Some participants have offered hints and suggestions for approaching the problem, including the use of polar coordinates. The discussion appears to be progressing with participants expressing gratitude for the guidance provided.
There is an emphasis on the need to solve for z^2 = i and z^2 = -i, indicating that participants are working within the constraints of complex number solutions.
So you know that z^2+ i= 0 and z^2- i= 0. Now you need to solve z^2= i and z^2= -i.wam_mi said:Homework Statement
Happy New Year, everybody!
Problem: Solve (z^4)+1 = 0
Homework Equations
The Attempt at a Solution
Attempt: (z^4)+1 = 0
((z^2)+i)*((z^2)-i) = 0
Could anyone help me to complete this question please?
Many Thanks!
HallsofIvy said:So you know that z^2+ i= 0 and z^2- i= 0. Now you need to solve z^2= i and z^2= -i.
You can, as Hootenanny suggested, write i and -i in "polar form" and use the fact that
[tex]\left(re^{i\theta}\right)^{1/2}= r^{1/2} e^{i\theta/2}[/tex]
HallsofIvy said:So you know that z^2+ i= 0 and z^2- i= 0. Now you need to solve z^2= i and z^2= -i.
You can, as Hootenanny suggested, write i and -i in "polar form" and use the fact that
[tex]\left(re^{i\theta}\right)^{1/2}= r^{1/2} e^{i\theta/2}[/tex]