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If |z| < sqrt(2)-1,t h e n|z^2+2zcosalph...

If `|z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s` a. less than 1 b. `sqrt(2)+1` c.`sqrt(2)-1` d. none of these

A

1

B

`sqrt(2)+1`

C

`sqrt(2)-1`

D

`sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`|z^(2)+2zcosalpha| le |z^(2)|+|2zcosalpha|`
`rArr |z^(2)+2zcosalpha|le |z|^(2)+2|z||cosalpha|`
`rArr |z^(2)+2zcosalpha| le |z|^(2)+2|z|`
`rArr |z^(2)+2zcosalpha| lt 1`
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Chapter Test
  1. If |z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s a. less than 1 b. sqr...

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  2. The locus of the center of a circle which touches the circles |z-z1|=a...

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  3. Prove that for positive integers n(1) and n(2), the value of express...

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  4. The value of abs(sqrt( 2i) - sqrt(2i)) is :

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  5. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

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  6. The value of ((1+ i sqrt(3))/(1-isqrt(3)))+ ((1-isqrt(3))/(1+isqrt(3)...

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  7. If alpha+ibeta=tan^(-1) (z), z=x+iy and alpha is constant, the locus o...

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  8. If cosA+cosB+cosC=0,sinA+sinB+sinC=0andA+B+C=180^(@) then the value of...

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  9. Find the sum 1xx(2-omega)xx(2-omega^(2))+2xx(-3-omega)xx(3-omega^(2))+...

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  10. The value of the expression (1+(1)/(omega))+(1+(1)/(omega^(2)))+(2+(1)...

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  11. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

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  12. The expression (1+i)^(n1)+(1+i^(3))^(n2) is real iff

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  13. If |{:(6i,3i,1),(4,3i,-1),(20,3,i):}|=x+iy, then (x, y) is equal to

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  14. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

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  15. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

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  16. Sum of the series sum(r=0)^n (-1)^r ^nCr[i^(5r)+i^(6r)+i^(7r)+i^(8r)] ...

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  17. If az(1)+bz(2)+cz(3)=0 for complex numbers z(1),z(2),z(3) and real num...

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  18. If 2z1-3z2 + z3=0, then z1, z2 and z3 are represented by

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  19. If Re((z+4)/(2z-1)) = 1/2 then z is represented by a point lying on

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  20. The vertices of a square are z(1),z(2),z(3) and z(4) taken in the anti...

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  21. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

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