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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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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. If |z(1)|=|z(2)|=………….=|z-(n)|=1, then the value of |z(1)+z(2)+………+z(n...

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  2. If omega(ne 1) be a cube root of unity and (1+omega)^(7)=A+Bomega, the...

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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. Let z and omega be two non-zero complex numbers, such that |z|=|omega|...

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  5. If z ne 0 be a complex number and "arg"(z)=pi//4, then

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  6. (1+i)^8+(1-i)^8=?

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  7. What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n...

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  8. If alphaand betaare different complex numbers with |beta|=1,then fin...

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  9. For any complex number z, the minimum value of |z|+|z-1|

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  10. If (3pi)/(2) gt alpha gt 2 pi, find the modulus and argument of (1 -...

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  11. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Argand plane, then...

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  12. Area of the triangle formed by 3 complex numbers, 1+i,i-1,2i, in the A...

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  13. If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6...

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  14. The locus represented by the equation |z-1| = |z-i| is

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  15. If z=i log(23,t h e ncosz= -1 b. -1//2 c. 1 d. 1//2

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  16. If alpha=cos alpha+i sin alpha, b=cos beta+isin beta,c=cos gamma+i sin...

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  17. lf z1,z2,z3 are vertices of an equilateral triangle inscribed in the c...

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  18. The general value of theta which satisfies the equation (costheta+isin...

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  19. If z is a complex numbers such that z ne 0 and "Re"(z)=0, then

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  20. If z + z^(-1)= 1, then find the value of z^(100) + z^(-100).

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