Home
Class 12
MATHS
If x(r)=cos. (pi)/(2^(r))+ isin. (pi)/(2...

If `x_(r)=cos. (pi)/(2^(r))+ isin. (pi)/(2^(r))`, then `x_(1)x_(2)x_(3)....oo=`

A

1

B

-1

C

-2

D

`-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMMON ENTRANCE TEST -2016

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|60 Videos
  • COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|297 Videos

Similar Questions

Explore conceptually related problems

If z_(k)=cos.(pi)/(2^(k))+isin.(pi)/(2^(k)) , k=1,2............ , then the value of z_(1)z_(2) ...............to oo is

If z_r=cos(pi/(3_r))+isin(pi/(3_r)),r=1,2,3, , prove that z_1z_2z_3 z_oo=idot

If cos ^(-1) x+sin ^(-1) (x)/(2)=(pi)/(6) then x=

If (1+x+x^(2))^(n) = sum_(r=0)^(2 n) a_(r). x^(r) then a_(1)-2 a_(2)+3 a_(3)-..-2 n. a_(2n) =

cos ((3pi)/( 4) + x) - cos((3pi)/( 4) -x) =- sqrt2 sin x

If (1+2 x+x^(2))^(n)=sum_(r=0)^(2 n) a_(r) x^(r) , then a_(r) =

(cos (pi +x) cos (-x))/( sin (pi -x) cos ((pi )/(2) + x))= cot ^(2) x

lim_(x rarr pi/3) (sin (pi/3-x))/(2 cos x-1) =

lim_(n to oo) sum_(r = 1)^(n) 1/n sin(r pi)/(2pi) is :

HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. If (z-1)/(z+1) is purely imaginary, then |z|=

    Text Solution

    |

  2. For any integer n, the argument of ((sqrt(3)+i)^(4 n+1))/((1-i sqrt(3)...

    Text Solution

    |

  3. If x(r)=cos. (pi)/(2^(r))+ isin. (pi)/(2^(r)), then x(1)x(2)x(3)....oo...

    Text Solution

    |

  4. If z(1)=1+i sqrt(3) , z(2)=1-i sqrt(3), then (z(1)^(100)+z(2)^(100))/(...

    Text Solution

    |

  5. If z(1)=1+i, z(2)=sqrt(3)+i, then arg ((z(1))/(z(2)))^(50)=

    Text Solution

    |

  6. If 1,a(1), a(2). ..., a(n-1) are n roots of unity, then the value of (...

    Text Solution

    |

  7. If z is such that |z-2 i|=2 sqrt(2), then arg ((z-2)/(z+2))=

    Text Solution

    |

  8. If |z(1)-1|lt2,|z(2)-2|lt1, then |z(1)+z(2)|

    Text Solution

    |

  9. If z(1) and z(2) are two non-zero complex numbers such that |z(1)+z(2)...

    Text Solution

    |

  10. The number i^(i) is

    Text Solution

    |

  11. The complex number z has argument, 0ltthetalt(pi)(2) and satisfy the e...

    Text Solution

    |

  12. If z(1) and z(2) are two non-zero complex numbers such that |z(1)+z(2)...

    Text Solution

    |

  13. The inequality |z-4|lt|z-2| represents the region given by

    Text Solution

    |

  14. The smallest positive integer n for which (1+i sqrt(3))^(n / 2) is rea...

    Text Solution

    |

  15. If x^(2)+x+1=0, then sum(r=1)^(2005)(x^(r)+(1)/(x^(r)))^(3)=

    Text Solution

    |

  16. If z(1), z(2), z(3) be vertices of an equilateral triangle occurring ...

    Text Solution

    |

  17. If z(1), z(2) are two complex numbers such that Im(z(1)+z(2))=0 and Im...

    Text Solution

    |

  18. If alpha is an imaginary fifth root of unity then log (2)|1+alpha+alph...

    Text Solution

    |

  19. If |z+bar(z)|+|z-bar(z)|=8 then z lies on

    Text Solution

    |

  20. The equation |z+i|-|z-i|=k represents a hyperbola, if

    Text Solution

    |