minimum value of modulus of (a+bω+cω² ),wherea,b,c r all not equal integers & ( ω is not equal to 1) is a cubic root of unity is....(IIT-JEE-2005)

please give detail explanation with every step...

Dear Rishi

 

 

steps

1 put value of w and w2

2 arange in x+iy form

3 use modulus formula

4 simplify it

5 since number are integer and not all equal so take a=b=1 it will make one bracket zero and and take c=2

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