Cube roots of unity:
|
For n = 3, we obtain the cube roots of unity and they are  + They are usually shown by 1, ω and ω2 and geometrically shown by the vertices of an equilateral triangle whose circumradius is unity and circumcentre is origin.
|
|
Note:
- ω3 = 1 and 1 + ω + ω2 = 0
- It can be easily proved that
1 + ωn + ω2n = 3 (n is a multiple of 3)
1 + ωn + ω2n = 0 (n is an natural number, not a multiple of 3)
Problem: Provided z1 + z2 + z3 = A ,
z1 + z2w + z3w2 = B
z1 + z2w2 + z3w = C
where w is cube root of unity.
Express z1, z2, z3 in term of A, B , C.
Solution: Adding three condition
z1 = A+B+C/3
Multiplying z1 + z2 + z3 = A, z1 + z2w + z3w2 = B, z1 + z2w2 + z2w = C by 1 , w2 ,w and adding we obtain
Email based Cube roots of unity Assignment Help -Cube roots of unity Homework Help
We at www.expertsmind.com offer email based Cube roots of unity assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.
Expertsmind's best education services
- Quality assignment-homework help assistance 24x7 hrs
- Best qualified tutor's network
- Time on delivery
- Quality assurance before delivery
- 100% originality and fresh work