Thread: cube root of unity..compex number

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.

Originally Posted by Shivanand

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

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.

Originally Posted by Shivanand

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.

CB