this question asked so many time in final year exam ,, but we were not able to solve this...... If 1,w,w^2 are the cube roots of unity, then find the roots of (z – 2)3 + 27 = 0.
this question asked so many time in final year exam ,, but we were not able to solve this...... If 1,w,w^2 are the cube roots of unity, then find the roots of (z – 2)3 + 27 = 0.
If:
rearrange this to:
so:
where is a cube root of unity is a root, so the required roots are:
CB
Last edited by CaptainBlack; Dec 16th 2008 at 03:50 AM.
If 1,w,w^2 are the cube roots of unity, then find the roots of (z – 2)^3 + 27 = 0. Plz ellaborate ur answer ,i am unable to understand . and also tell me from where can i find information for this.
If 1,w,w^2 are the cube roots of unity, then find the roots of (z – 2)^3 + 27 = 0. Plz ellaborate ur answer ,i am unable to understand . and also tell me from where can i find information for this.
If:
so:
but only three of the exponential terms on the right are distinct and these are the cube roots of , and the three distinct values are , , , from which the previous result follows.
This uses Eulers formula for complex numbers and the laws of powers.