Question

solve the complex equation z^4+z^2+1=0

Answer 1

Given complex equation is z^4+z^2+1 = 0

Let z^2 = x

Now the equaton is x^2+x+1 = 0

Compare it quadratic equation form ax^2+bx+c = 0

a = 1, b = 1, c = 1

Roots are x = [-b±√(b^2-4ac)]/2a

x = [-1±√(1-4*1*1)]/2*1

x = [-1±√(1-4)/2

x = [-1±√-3]/2

x = [-1±√3i]/2

z^2 = [-1±√3i]/2

z = sqrt[-1±√3i]/2