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Let omega be the complex number cos((2...

Let `omega` be the complex number `cos((2pi)/3)+isin((2pi)/3)`. Then the number of distinct complex cos numbers z satisfying `Delta=|(z+1,omega,omega^2),(omega,z+omega^2,1),(omega^2,1,z+omega)|=0` is

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The correct Answer is:
1
(1) `omega =e^(i2pi//3)`
`|{:(,z+1,omega,omega^(2)),(,omega,z+omega^(2),1),(,omega^(2),1, z+omega):}|=0`
Applying `(C_(1) to C_(1) + C_(2) + C_(3))`
`|{:(,1,omega,omega^(2)),(,omega,z+omega^(2),1),(,1,1, z+omega):}|=0`
`rArr z^(3) = 0`
z= 0 is only solutions.
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