How can I find the rules for deriving a complex number without a complex root?

Click For Summary
The discussion revolves around finding the rules for deriving a complex number without a complex root, specifically focusing on the cube root of -9 + 46i. Participants suggest using trigonometric form and De Moivre's theorem for easier calculations, noting that every complex number has three distinct roots. There are references to historical methods, including Bombelli's solution, and the importance of understanding the relationship between the components of complex numbers. Some users express a desire for clarity on how to multiply vectors in the context of complex numbers and the historical significance of these mathematical concepts. The conversation highlights the complexity of deriving roots and the various methods available for solving such problems.
  • #31
There is no complex root. Two roots coincide, x1=x2=-3, x3=6.

ehild
 
  • Like
Likes 1 person

Similar threads

Complex numbers problem |z| - iz = 1-2i
  • · Replies 20 ·
Replies
20
Views
2K
Help Checking a Complex Numbers Problems
  • · Replies 7 ·
Replies
7
Views
3K
How Do You Solve Complex Number Equations in Quadratics and Exponentials?
  • · Replies 39 ·
2
Replies
39
Views
5K
How to find z^n of a complex number
  • · Replies 12 ·
Replies
12
Views
3K
Adding square roots of ##i## leading to different answers!
  • · Replies 21 ·
Replies
21
Views
2K
Solving an equation with fractional part function
  • · Replies 5 ·
Replies
5
Views
2K
Domain of a Function: Real vs Complex Numbers
  • · Replies 5 ·
Replies
5
Views
2K
Complex Number Equations: Solving for z and Finding the Perpendicular Bisector
  • · Replies 31 ·
2
Replies
31
Views
3K
How to represent this complex number?
  • · Replies 18 ·
Replies
18
Views
3K
I Questions about the arg of complex numbers
  • · Replies 4 ·
Replies
4
Views
2K