• Support PF! Buy your school textbooks, materials and every day products Here!

Right triangle with complex vertices

  • Thread starter zelmac
  • Start date
  • #1
5
0

Homework Statement


Find the geometric image of the complex number z, if [tex]z, z^2, z^3[/tex] are the vertices of a right triangle.


Homework Equations





The Attempt at a Solution



I tried expanding [itex]z^2, z^3[/itex], and than using both the pythagoras theorem, and vectors (in separate attempts), but failed to get at a solution.

All help is very appreciated :)
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,848
1,645
These are the vertices of a right triangle in the complex plain right?
So this is basically a vector addition/subtraction problem.
Each side is the difference between two position vectors.

Figure out which is the hypotenuse and then you need only set the angle between the other two sides to [itex]\pi/2[/itex].
 

Related Threads on Right triangle with complex vertices

Replies
8
Views
8K
  • Last Post
Replies
3
Views
1K
Replies
2
Views
1K
Replies
7
Views
2K
  • Last Post
Replies
7
Views
2K
Replies
8
Views
1K
Replies
6
Views
1K
  • Last Post
Replies
6
Views
6K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
7
Views
5K
Top