Home
Class 12
MATHS
If (1 + i)(1 + 2i)(1 + 3i)….(1 + ni) = x...

If (1 + i)(1 + 2i)(1 + 3i)….(1 + ni) = x + iy, then 2.5.10…`(1 + n^(2))`is

A

1

B

i

C

`x^(2)+y^(2)`

D

`1 + n^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS (1 MARK)|20 Videos

  • COMPLEX NUMBERS

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS (FILL IN THE BLANKS)|10 Videos

  • COMPLEX NUMBERS

    SURA PUBLICATION|Exercise EXERCISE 2.8|16 Videos

  • APPLICATIONS OF VECTORA ALGEBRA

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS ( 5 MARKS )|5 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    SURA PUBLICATION|Exercise 5 MARKS|4 Videos

Similar Questions

Explore conceptually related problems

If (1+i)(1+2i)(1+3i)"……."(1+ni)=a+ib," then "2xx5xx10xx"………"xx(1+n^2) is equal to

If ((1 + i)/(1 - i))^(3) - ((1 - i)/(1 + i))^(3) = x + iy then (x, y) = …….

Find z^(-1) , if z = ( 2 +3i)(1-i)

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i_5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :

The value of (1 + i)( 1 + i^(2) ) (1 + i^(3)) (1 + i^(4)) is

If z_1 = 4 - 7i , z_2 = 2 + 3i and z_3 = 1 + i show that z_1 + (z_2 + z_3) = (z_1 + z_2)+z_3

If i^(2) = -1 , then i^(1) + i^(2) + i^(3) + ….. + up to 1000 terms is equal to

i^(n) + i^(n+1) + i^(n + 2) + i^(n + 3)

a+ib=(1+i)(1+2i)(1+3i) then a^(2)+b^(2)=

SURA PUBLICATION-COMPLEX NUMBERS-EXERCISE 2.9
  1. If z is non zero complex number, such that 2i z^(2) = bar(z),then |z| ...

    Text Solution

    |

  2. If |z-2 + i|le2, then the greatest value of |z| is

    Text Solution

    |

  3. If |z - (3)/(z)| = 2, then the least value of |z| is

    Text Solution

    |

  4. If |z| = 1, then the value of (1+z)/(1 +bar(z)).

    Text Solution

    |

  5. The solution of the equation |z| -z = 1 + 2i is

    Text Solution

    |

  6. If |z(1)| = 1, |z(2)| = 2, |z(3)| = 3 and |9z(1)z(2) + 4z(1) z(3) + z(...

    Text Solution

    |

  7. If z is a complex number such that z in CC\\RR, and z + (1)/(z) in RR,...

    Text Solution

    |

  8. z(1), z(3), and z(3) are complex numbers such that z(1) + z(2) + z(3)=...

    Text Solution

    |

  9. If (z - 1)/(z + 1) is purely imaginary, then |z| is

    Text Solution

    |

  10. If z = x + iy is a complex number such that |z + 2| = |z - 2|, then th...

    Text Solution

    |

  11. The principal argument of (3)/(-1 + i) is

    Text Solution

    |

  12. The principal argument of (sin 40^(@) + i cos 40^(@))^(5) is

    Text Solution

    |

  13. If (1 + i)(1 + 2i)(1 + 3i)….(1 + ni) = x + iy, then 2.5.10…(1 + n^(2))...

    Text Solution

    |

  14. If omega ne 1 is a cubic root of unit and (1 + omega)^(7) = A + Bomega...

    Text Solution

    |

  15. The principal argument of the complex number ((1 + i sqrt(3))^(2))/(4i...

    Text Solution

    |

  16. If alpha and beta are the roots of x^(2) + x + 1 = 0, then alpha^(2020...

    Text Solution

    |

  17. The product of all four values of (cos"" (pi)/(3) + i sin ""(pi)/(3))^...

    Text Solution

    |

  18. If omega ne 1 is a cubit root unity and |(1,1,1),(1,-omega^(2)-1,omega...

    Text Solution

    |

  19. The value of ((1+sqrt(3)i)/(1 - sqrt(3)i))^(10) is

    Text Solution

    |

  20. If omega = cis (2pi)/(3), then number of distinct roots of |(z+1,omega...

    Text Solution

    |