Home
Class 11
MATHS
Which of the following is correct for an...

Which of the following is correct for any tow complex numbers `z_1a n dz_2?` (a)`|z_1z_2|=|z_1||z_2|` (b) `a r g(z_1z_2)=a r g(z_1)a r g(z_2)` (c) `|z_1+z_2|=|z_1|+|z_2|` (d) `|z_1+z_2|geq|z_1|+|z_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

Which of the following is correct for any tow complex numbers z_1a n dz_2? |z_1z_2|=|z_1||z_2| (b) a r g(z_1z_2)=a r g(z_1)a r g(z_2) (c) |z_1+z_2|=|z_1|+|z_2| (d) |z_1+z_2|geq|z_1|+|z_2|

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|lt=|z_1|+|z_2|

For any two complex number z_1a n d\ z_2 prove that: |z_1+z_2|geq|z_1|-|z_2|

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|geq|z_1|-|z_2|

For any two complex numbers z_1 and z_2 , we have |z_1+z_2|^2=|z_1|^2+|z_2|^2 , then

For any two complex numbers z_1 and z_2 , we have |z_1+z_2|^2=|z_1|^2+|z_2|^2 , then

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2=|\z_1|^2+|\z_2|^2+2Re bar z_1 z_2

For any two complex numbers z_(1) and z_(2) |z_(1)+z_(2)|^(2) =(|z_(1)|^(2)+|z_(2)|^(2))

If for the complex numbers z_1 and z_2 , |z_1+z_2|=|z_1-z_2| , then Arg(z_1)-Arg(z_2) is equal to

For any two complex numbers z_1 and z_2 , prove that Re(z_1z_2)=Re(z_1) Re(z_2)-Im(z_1) Im(z_2) .

RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. Perform the indicated operation and find the result in the form a+i bd...

    Text Solution

    |

  2. Let z1=2-i ,""""z2=-2+i . Find (i) Re ((z1z2)/( bar z1)) (ii) Im(1...

    Text Solution

    |

  3. Which of the following is correct for any tow complex numbers z1a n dz...

    Text Solution

    |

  4. If z1a n dz2 are two complex numbers such that |z1|=|z2|a n d arg(z1)...

    Text Solution

    |

  5. Evaluate sum(n=1)^(13)(i^n+i^(n+1)), where n in Ndot

    Text Solution

    |

  6. Evaluate 1+i^2+i^4+i^6+...+i^(2n)dot

    Text Solution

    |

  7. Show that: {i^(19)+(1/i)^(25)}^2=-4 (ii) {i^(17)-(1/i)^(34)}^2=2i (ii...

    Text Solution

    |

  8. If z1, z2 in C , then say which are true and false - ...

    Text Solution

    |

  9. Prove that the following complex number is purely real: (i)((2+3i)/(3+...

    Text Solution

    |

  10. Show that 1+i^(10)+i^(20)+i^(30) is a real number.

    Text Solution

    |

  11. Find the values of following expression:1+i^2+i^4+i^6+i^8+doti^(20)

    Text Solution

    |

  12. If (a+i b)(c+i d)(e+if)(g+i h)=A+i B prove that (a^2+b^2)(c^2+d^2)(e...

    Text Solution

    |

  13. If z1, z2 are complex number such that (2z1)/(3z2) is purely imaginary...

    Text Solution

    |

  14. If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

    Text Solution

    |

  15. If z is a complex number such that |z|=1, prove that (z-1)/(z+1) is pu...

    Text Solution

    |

  16. If z=x+i y and w=(1-i z)/(z-i) , show that |w|=1 z is purely real.

    Text Solution

    |

  17. If z=2-3i show that z^2-4z+13=0 and hence find the value of 4z^3-3z^...

    Text Solution

    |

  18. If |z1|=|z2|=.......=|zn|=1, prove that |z1+z2+z3++zn|=1/(z1)+1/(z2)+...

    Text Solution

    |

  19. Find the non-zero complex numbers z satisfying barz =i z^2dot

    Text Solution

    |

  20. Show that if iz^3+z^2-z+i=0, then |z|=1

    Text Solution

    |