Home
Class 11
MATHS
If n is a positive integer, prove that |...

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

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

If x and y are positive real numbers and m, n are any positive integers, then prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4

If m and n are positive integers, then prove that the coefficients of x^(m) " and " x^(n) are equal in the expansion of (1+x)^(m+n)

If m,n,r are positive integers such that r lt m,n, then ""^(m)C_(r)+""^(m)C_(r-1)""^(n)C_(1)+""^(m)C_(r-2)""^(n)C_(2)+...+ ""^(m)C_(1)""^(n)C_(r-1)+""^(n)C_(r) equals

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

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 :

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 :

If n is a positive integer greater than unity z is a complex number satisfying the equation z^n=(z+1)^n, then

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. For x in (0,1) , prove that i^(2i+3) ln((i^3x^2+2x+i)/(i x^2+2x+i^3))=...

    Text Solution

    |

  2. The sum of the non-real root of (x^2+x-2)(x^2+x-3)=12 is -1 b. 1 c. -...

    Text Solution

    |

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

    Text Solution

    |

  4. The number of roots of the equation sqrt(x-2)(x^2-4x+3)=0 is (A) Thre...

    Text Solution

    |

  5. If z1, z2a n dz3, z4 are two pairs of conjugate complex numbers, then ...

    Text Solution

    |

  6. Prove that following inequalities: |z/(|z|)-1|lt=|a rgz| (ii) |z-1|lt=...

    Text Solution

    |

  7. If x=1+i is a root of the equation =x^3-i x+1-i=0, then the other real...

    Text Solution

    |

  8. Find the modulus, argument, and the principal argument of the complex ...

    Text Solution

    |

  9. Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))...

    Text Solution

    |

  10. Column I, Column II: possible argument of z=a+i b a b >0 , p. tan^(...

    Text Solution

    |

  11. If the expression x^2+2(a+b+c)+3(b c+c+a b) is a perfect square, then ...

    Text Solution

    |

  12. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4a n d ...

    Text Solution

    |

  13. The curve y=(lambda+1)x^2+2 intersects the curve y=lambdax+3 in exac...

    Text Solution

    |

  14. Column I, Column II (one of the values of z ) z^4-1=0 , p. z=cospi/...

    Text Solution

    |

  15. Let za n dw be two nonzero complex numbers such that |z|=|w|a n d arg...

    Text Solution

    |

  16. The number of irrational roots of the equation (4x)/(x^2+x+3)+(5x)/(x^...

    Text Solution

    |

  17. If |z+barz|+|z-barz|=2 then z lies on (a) a straight line (b) a set of...

    Text Solution

    |

  18. If one vertex of the triangle having maximum area that can be inscribe...

    Text Solution

    |

  19. The number of complex numbers z satisfying |z-3-i|=|z-9-i|a n d|z-3+3i...

    Text Solution

    |

  20. If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots a...

    Text Solution

    |