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If z1,z2 and z3,z4 are two pairs of conj...

If `z_1,z_2` and `z_3,z_4` are two pairs of conjugate complex numbers then `arg(z_1/z_4)+arg(z_2/z_3)=`

A

0

B

`pi//2`

C

`3pi//2`

D

`pi`

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A
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. The value of sum(r=1)^(8)(sin(2rpi)/9+icos(2rpi)/9), is

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  2. If z(1),z(2),z(3),…………..,z(n) are n nth roots of unity, then for k=1,2...

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  3. If z1,z2 and z3,z4 are two pairs of conjugate complex numbers then arg...

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  4. If |z(1)|=|z(2)| and arg (z(1))+"arg"(z(2))=0, then

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  5. If one vertex of a square whose diagonals intersect at the origin is 3...

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  6. The value of z satisfying the equation logz+logz^(2)+……..+logz^(n)=0...

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  7. If |z(1)|=|z(2)|=………….=|z-(n)|=1, then the value of |z(1)+z(2)+………+z(n...

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

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

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

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

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  12. (1+i)^8+(1-i)^8=?

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

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

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

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

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

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

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

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

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