Home
Class 11
MATHS
Let z1=2-i ,""""z2=-2+i . Find (i) Re (...

Let `z_1=2-i ,""""z_2=-2+i` . Find (i) Re `((z_1z_2)/( bar z_1))` (ii) Im`(1/(z_1 bar z_1))`

Text Solution

Verified by Experts

Here `z_1=2-i, z_2=-2+i`

:. `overline z_1=2+i`

(i) Now `z_1z_2=(2-i)(-2+i)=-4+2i+2i+i^2` ...
Promotional Banner

Topper's Solved these Questions

  • COMBINATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|117 Videos
  • DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|236 Videos

Similar Questions

Explore conceptually related problems

Let z_(1)=2-i,z_(2)=-2+i* Find (i) Re ((z_(1)z_(2))/(bar(z)_(1))) (ii) Im quad ((1)/(z_(1)bar(z)_(1)))

Let z_(1)=2-i,z_(2)=-2+i find (a)Re((z_(1)z_(2))/(z_(1)))

if z_(1) = 3-i and z_(2) = -3 +i, then find Re ((z_(1)z_(2))/(barz_(1)))

If z_(1)=2-i,quad +2=-2+i, find :Re((z_(1)z_(2))/(z_(1)))

if z_(1)=1-i and z_(2) = -2 + 4i then find Im((z_(1)z_(2))/barz_(1))

If z_(1)=2-i,+2=-2+i, find :Im((1)/(z_(1)(z)_(2)))

If z_(1)=2-i, z_(2)=1+ 2i, then find the value of the following : (i) Re((z_(1)*z_(2))/(bar(z)_(2))) (ii) Im (z_(1)*bar(z)_(2))

If z_(1)=1-i,z_(2)=-2+4i, Find the Modulus of Z=(Z_(1)*Z_(2))/(bar(z)_(1))

If z_(1)=2-i,z_(2)=1+i, find |(z_(1)+z_(2)+1)/(z_(1)-z_(2)+i)|

If ,z_(1)=,2-i,z_(2)=1+i find ,,|(z_(1)+z_(2)+1)/(z_(1)-z_(2)+i)|

RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. If (1+i)(1+2i)(1+3i)........(1+n i)=a+i b ,t h e n2xx5xx10 ....(1+n^2)...

    Text Solution

    |

  2. Perform the indicated operation and find the result in the form a+i bd...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Find the value of 1+i^(2)+i^(4)+i^(6)+...+i^(2n),

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Find the values of following expressions: i^(49)+i^(68)+i^(89)+i^(110)...

    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

    |