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If (omega ne1) is a cube root of unity ,...

If `(omega ne1)` is a cube root of unity , then
`{:(1 , 1 + i+ omega^(2) , omega^(2)) , (1-i, -1 , omega^(2) -1) , (-i , -1 + omega - i, -1):}|

A

Zero

B

1

C

`i`

D

`omega`

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The correct Answer is:
A
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. If omega is a complex cube root unity then sin { (omega^(10) + omega^(...

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  2. If z + (1)/(z) = -1 then z^(5) + (1)/(z^(5)) =

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  3. If (omega ne1) is a cube root of unity , then {:(1 , 1 + i+ omega^(2...

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  4. If n (ne 3) is an integer and z = -1 + isqrt3 , then z^(2n) + 2^(n) ,...

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  5. If |(z - 4bari)/(z-2)| = 2 then the locus of z is

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  6. The locus of the point z=x+iy satisfying |(z-2i)/(z+2i)|=1 is

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  7. If |z| = sqrt2 then the point given by "3 + 4z" lies on a circle whos...

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  8. The complex equation |z + 1- i| = |z + i-1| represents a

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  9. If z = x + iy is a complex numbers z for which |z +i//2|^(2) = |z - i/...

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  10. If |z + barz| + |z - barz| = 2 then z lies on

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  11. If |z^(2) - 1| = |z|^(2) + 1 , then z lies on

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  12. If omega is a complex cube root of unity , then sum(k = 1)^(6) ( omega...

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  13. If z(barz+3)=2 then the locus of z = x + iy is

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  14. If alpha + ibeta = tan^(-1) (z) , z = x +iy and alpha is constant then...

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  15. If (z - i)/(z +1) is purely imaginary then the locus of z = x +iy is

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  16. If log (tan 30^(@)) ( (2 |z|^(2) + 2 |z| - 3)/(|z| + 1)) lt -2 , then

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  17. The locus of z satisfying the inequality log ((1)/(3)) |z + 1| gt log(...

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  18. If z(1) = 8 + 4i , z(2) = 6 + 4i and z be a complex number such that ...

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  19. The triangle formed by the points 1 , (1 +i)/(sqrt2) and ias vertices ...

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  20. If |z| =3 , the area of the triangle whose sides are z , omega z and ...

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