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If omega is the complex cube root of uni...

If `omega` is the complex cube root of unity then ` |[1,1+i+omega^2,omega^2],[1-i,-1,omega^2-1],[-i,-i+omega-1,-1]|=`

A

0

B

1

C

i

D

`omega`

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MCGROW HILL PUBLICATION-COMPLEX NUMBERS -EXERCISE LEVEL 1
  1. If omega is a cube root of unity then find the value of sin((omega^(10...

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  2. If omega (ne 1) is a cube root of unity and (1 + omega)^(2017) = A + B...

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  3. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

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  4. If omega is an imaginary cube root of unity, then (1-omega-omega^(2))^...

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  5. If |{:(6i,-3i,1),(4,3i,1),(20,3,i):}|=x+iy,i=sqrt(-1) then

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  6. If arg(z) lt 0, then find arg(-z) -arg(z).

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  7. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

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  8. Let z1 and z2 be nth roots of unity which subtend a right angle at the...

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  9. The complex number z1,z2 and z3 satisfying (z1 - z3)/(z2 - z3) = ( 1 -...

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  10. Let omega = - (1)/(2) + i (sqrt3)/(2), then the value of the determina...

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  11. The inequality |z-i| lt |z + i| represents the region

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  12. Show that if iz^3+z^2-z+i=0, then |z|=1

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  13. If x + iy = (1)/(1-cos theta + 2 i sin theta), theta ne 2n pi, n in I,...

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  14. The equation z^3=bar z has

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  15. If z = 5 + t + isqrt(25 - t^(2)), (-5 le t le 5), then locus of z is a...

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  16. If omega is complex cube root of that 1/(a+omega)+1/(b+omega)+1/(c+ome...

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  17. if |z-iRe(z)|=|z-Im(z)| where i=sqrt(-1) then z lies on

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  18. If omega is a complex cube root of unity, then value of expression cos...

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  19. If roots of the equation z^2+ az + b = 0 are purely imaginary then

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  20. The system of equations |z+1-i|=sqrt2 and |z| = 3 has

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