Home
Class 11
MATHS
If xr = cos(pi/3^r)+isin (pi/3^r) : prov...

If `x_r = cos(pi/3^r)+isin (pi/3^r)` : prove that `x_1x_2x_3`....upto infinity=i

Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

If x_r=cos(pi/2^r)+isin(pi/2^r) then x_1x_2x_3.......infty =

If a=cos((4pi)/3)+isin((4pi)/3) then ((1+a)/2)^3n is

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .

If tanx+tan(x+pi/3)+tan(x+(2pi)/3)=3 then prove that (3tanx-tan^3x)/(1-3tan^2x)=1

f(x)=cos^2x+cos^2(pi/3 +x)-cosxcos(pi/3 +x) is

Convert the complex number z=(i-1)/(cos(pi/3)+isin(pi/3)) in the polar form.

If f(x) = sin^(-1) x then prove that lim_(x rarr (1^(+))/(2)) f(3x -4x^(3)) = pi - 3 lim_(x rarr (1^(+))/(2)) sin^(-1) x

If cos(pi/7), cos((3pi)/7), cos((5pi)/7) are the roots of the equation 8x^3-4x^2-4x+1=0 The value of sec(pi/7)+sec((3pi)/7)+sec((5pi)/7) is

Prove that cos ((pi)/(4) + x) + cos ((pi)/(4) -x) = sqrt2 cos x

If f(x)=sin^(-1)x then prove that lim_(x->1/2)f(3x-4x^3)=pi-3lim_(x->1/2)sin^(-1)x

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. If in argand plane the vertices A,B,C of an isoceles triangle are rep...

    Text Solution

    |

  2. Find the square root of -7-24i

    Text Solution

    |

  3. If xr = cos(pi/3^r)+isin (pi/3^r) : prove that x1x2x3....upto infinity...

    Text Solution

    |

  4. if alpha, beta, gamma are roots of x^3-3x^2+3x+7=0, then find (alpha-1...

    Text Solution

    |

  5. If alpha1,alpha2....alpha(n-1) are the nth roots of unity then show th...

    Text Solution

    |

  6. Show that the points represented by complex numbers (3+2i),(2-i),-7i a...

    Text Solution

    |

  7. Find the centre and radius of circle 2absz^2+(3-i)z +(3+i)barz-7=0

    Text Solution

    |

  8. Find all the circles which are orthogonal to absz=1 and abs(z-1)=4

    Text Solution

    |

  9. If z1,z2,z3 are complex numbers such that 2/z1=1/z2 + 1/z3, show that ...

    Text Solution

    |

  10. If 4x+i(3x-y)=3+i(-6), where x and y are real numbers, then find the v...

    Text Solution

    |

  11. Find the multiplicative inverse of 2-3i.

    Text Solution

    |

  12. Convert the complex number (-16)/(1+isqrt3) into polar form.

    Text Solution

    |

  13. Find real theta such that (3+2isintheta)/(1-2isintheta) is purely real...

    Text Solution

    |

  14. Convert the complex number z=(i-1)/(cos(pi/3)+isin(pi/3)) in the polar...

    Text Solution

    |

  15. {1+(-i)^(4n+3)}(1-i), (ninN) equals

    Text Solution

    |

  16. If z1,z2 are conjugate complex numbers and z3,z4 are also conjugate, t...

    Text Solution

    |

  17. If z=(1+i)(1+sqrt 3i)^2/(1-i), then argz equal

    Text Solution

    |

  18. The equation z^3=barz has

    Text Solution

    |

  19. In the argand plane ABCD is a square described in the anticlockwise se...

    Text Solution

    |

  20. (-64)^(1/4) equals

    Text Solution

    |