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If one vertex of a square whose diagonal...

If one vertex of a square whose diagonals intersect at the origin is `3(costheta+isintheta)` , then find the two adjacent vertices.

A

`+-3(sintheta-isintheta)`

B

`+-(sintheta+icostheta`

C

`+-(costheta-isintheta)`

D

`z_(1)barz_(2)=1`

Text Solution

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The correct Answer is:
a
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Exercise
  1. If z(1),z(2) and z(3), z(4) are two pairs of conjugate complex numbers...

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

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

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  4. The value of z satisfying the equation logz+logz^2+dot+logz^n=0i s

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  5. If |z(1)|= |z(2)|= ….= |z(n)|=1, prove that |z(1) + z(2) + …+ z(n)|= |...

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  6. If omega is a cube root of unity and (1+omega)^7=A+Bomega then find th...

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  7. If omega(!=1) is a cube root of unity, then value of the determinant|1...

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

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

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  10. (1+i)^8+(1-i)^8=?

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

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  12. If alpha\ a n d\ beta are different complex numbers with |beta|=1,\ fi...

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

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

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  15. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Arg and plane, the...

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

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  17. If omega is a comples cube root of unity, then (1 - omega + omega^(2) ...

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

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  19. If z=i log(2-sqrt(3)) then cosz

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  20. If a=cos alpha+i sin alpha, b=cos beta+isin beta,c=cos gamma+i sin gam...

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