Complex roots (1 Viewer)

[Utility]

If w₁ = -√3 + i is a cube root of z. Find z. Is there any quick method to getting the original angle (arg(z))? I don’t understand that part, in particular.

 

[Autistic Chimp]

It has been a while since I did complex, but if (-√3+i)^3 = z, then z = 8i when you expand it, therefore arg(z)=pi/2. That's about 4 lines of working.

 

[Utility]

Yeah, pi / 2. I started doubting it after doing so many of them.

 

[RealiseNothing]

Cubing this, using De Moivre's Theorem, we will cube the modulus and multiply the argument by 3:



(note we just subtracted so it doesn't change anything).

 

[Nws m8]

Cubing this, using De Moivre's Theorem, we will cube the modulus and multiply the argument by 3:



(note we just subtracted so it doesn't change anything).

That's the right and quickest method, I think they teach you this method at school, don't they? ...