Home
Class 11
MATHS
If n is any positive integer, write the ...

If `n` is any positive integer, write the value of `(i^(4n+1)-i^(4n-1))/2` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMBINATIONS

    RD SHARMA ENGLISH|Exercise All Questions|117 Videos

  • DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|230 Videos

Similar Questions

Explore conceptually related problems

For a positive integer n , find the value of (1-i)^(n) (1 - 1/i)^(n)

If n is any integer, then the value of (-sqrt(-1))^(4n+3)

For a positive integer n , find the value of ( 1-i)^n(1-1/i)^ndot

If rArr I_(n)=int_(0)^(pi//4) tan ^(n)x dx , then for any positive integer, n, the value of n(I_(n+1)+I_(n-1)) is,

For a positive integer n , find the value of (1-i)^n(1-1/i)^ndot

If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1.)

If n is a positive integer, then ((n+4)!)/((n+7)!)=

If n is a positive integer then 2^(4n) - 15n - 1 is divisible by

If 4^(x)*n^(2)=4^(x+1)*n and x and n are both positive integers, what is the value of n?

For any integer n, the argument of ((sqrt3+i)^(4n+1))/((1-isqrt3)^(4n))

RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. If x+i y=sqrt((a+i b)/(c+i d)), then write the value of (x^2+y^2)^2.

    Text Solution

    |

  2. If pi < theta <2pi and z=1+costheta+isintheta , then write the value o...

    Text Solution

    |

  3. If n is any positive integer, write the value of (i^(4n+1)-i^(4n-1))/2...

    Text Solution

    |

  4. Write the value of (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+...

    Text Solution

    |

  5. Write 1-i in polar form.

    Text Solution

    |

  6. Write 1+isqrt(3)\ in polar form.

    Text Solution

    |

  7. Write the argument of idot

    Text Solution

    |

  8. Find the principal argument of (1+isqrt(3))^2dot

    Text Solution

    |

  9. Find z ,\ if\ |z|=4\ and \ arg(z)=(5pi)/6 where z represents a complex...

    Text Solution

    |

  10. Write the value of sqrt(-25)xxsqrt(-9)dot

    Text Solution

    |

  11. Write the value of a r g(z)+a r g( barz ) .

    Text Solution

    |

  12. If |z+4|lt=3 then find the greatest and least values of |z+1|dot

    Text Solution

    |

  13. For any two complex numbers z1\ a n d\ z2 and any two real numbers a ,...

    Text Solution

    |

  14. If n in NN ,then find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3).

    Text Solution

    |

  15. Find the real value of a for which 3i^3-2a i^2+(1-a)i+5 is real.

    Text Solution

    |

  16. If |z|=2 and arg (z)=pi/4 , find z.

    Text Solution

    |

  17. Write the argument of (1+isqrt(3))(1+i)(costheta+isintheta).

    Text Solution

    |

  18. The value of (1+i)(1+i^2)(1+i^3)(1+i^4) is a. 2 b. 0 c. 1 d. i

    Text Solution

    |

  19. If (3+2i sintheta)/(1-2i sintheta) is a real number and 0lt theta lt 2...

    Text Solution

    |

  20. If sqrt(a+i b)=x+i y ,\ then possible value of sqrt(a-i b) is a. x^2+...

    Text Solution

    |