Home
Class 11
MATHS
If (1+i)(1+2i)(1+3i)......(1+n i)=(x+i y...

If `(1+i)(1+2i)(1+3i)......(1+n i)=(x+i y)` , show that `2. 5. 10...... (1+n^2)=x^2+y^2dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

Given that (1 + i) (1 + 2i) (1 + 3i)…(1 + ni)= x+ iy , show that 2.5.10…(1 + n^(2))= x^(2) + y^(2)

If (1+i)(1+2i)(1+3i)...(1+n i)=a+i b , then the value of; 2. 5. 10. 17... (1+n^2\ ) will be (a) . a-i b (b) . a^2-b^2 (c) . a^2+b^2 (d) . none of these

If (1+i)(1+2i)(1+3i)1+m)=(x+i y) , then show that 2xx5xx10xxxx(1+n^2)=x^2+y^2dot

If ( 1+i) (1+ 2i) (1+ 3i) …(1 +ni) = x+ iy, then 2,5,10 ….( 1+n^(2)) = x^(k) +y^(k) The value of k is :

If x+ iy=(1+ 4i)(1+5i) , then (x^(2)+y^(2)) is equal to :

If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is: (a) . 0 (b) . 1 (c) . 100 (d) . none of these

If ((1+i)/(1-i))^(2) - ((1-i)/(1+i))^(2) = x + iy then find (x,y).

If (1+2i) (2+3i)(3+4i)=x+iy,x,y in R then x^(2)+y^(2) is

If z= x+ yi and (|z-1 -i|+4)/(3|z-1-i|-2)=1 , show that x^(2) + y^(2)- 2x-2y-7=0

Given that (1 + i)/(1 + 2^(2)i) xx (1 + 3^(2) i)/(1 + 4^(2) i) xx….xx (1 + (2n-1)^(2)i)/(1+(2n)^(2)i)= (a + bi)/(c+di) , show that (2)/(17) xx (82)/(257) xx ….xx ((2n-1)^(4) + 1)/((2n)^(4) + 1) = (a^(2) + b^(2))/(c^(2) + d^(2))

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let a is a real number satisfying a^3+1/(a^3)=18 . Then the value of a...

    Text Solution

    |

  2. Find non zero integral solutions of |1-i|^x=2^xdot

    Text Solution

    |

  3. If (1+i)(1+2i)(1+3i)......(1+n i)=(x+i y) , show that 2. 5. 10...... (...

    Text Solution

    |

  4. If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c<0 , then wh...

    Text Solution

    |

  5. If omega is a cube root of unity, then find the value of the following...

    Text Solution

    |

  6. If f(x)=sqrt(x^2+a x+4) is defined for all x , then find the values of...

    Text Solution

    |

  7. If omega is a cube root of unity, then find the value of the following...

    Text Solution

    |

  8. Find the domain and range of f(x)=sqrt(x^2-4x+6)

    Text Solution

    |

  9. Prove that |z1+z2|^2=|z1|^2+|z2|^2, ifz1//z2 is purely imaginary.

    Text Solution

    |

  10. Find the range of the function f(x)=6^x+3^x+6^(-x)+3^(-x)+2.

    Text Solution

    |

  11. If omega is a cube root of unity, then find the value of the following...

    Text Solution

    |

  12. If alpha ,beta are the roots of the equation 2x^2+2(a+b)x+a^2+b^2=0 th...

    Text Solution

    |

  13. Let z1,z2, z3, zn be the complex numbers such that |z1|=|z2|=|zn|=1. I...

    Text Solution

    |

  14. If a ,b , in R such that a+b=1a n d(1-2ab)(a^3+b^3)=12 . The value ...

    Text Solution

    |

  15. If |z|lt=4 , then find the maximum value of |i z+3-4i|dot

    Text Solution

    |

  16. Find the range of f(x)=x^2-x-3.

    Text Solution

    |

  17. If the fraction (x^3 +(a-10)x^2-x+a-6)/(x^3 +(a-6)x^2-x+a-10)reduces t...

    Text Solution

    |

  18. The polynomial f(x)=x^4+a x^3+b x^3+c x+d has real coefficients and f(...

    Text Solution

    |

  19. Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

    Text Solution

    |

  20. If the quadratic equation a x^2+b x+c=0(a >0) has sec^2thetaa n dcos e...

    Text Solution

    |