Home
Class 11
MATHS
Prove that (3+i)/(1+2i)+(3-i)/(1-2i) is ...

Prove that `(3+i)/(1+2i)+(3-i)/(1-2i)` is a real number.

Text Solution

Verified by Experts

The correct Answer is:
N/a
`(3+i)/(1+2i)+(3-i)/(1-2i)`
`" "=((3+i)(1-2i)+(3-i)(1+2i))/((1+2i)(1-2i))`
`" "=(3-6i+i-2i^(2)+3+6i-i-2i^(2))/(1-4i^(2))`
`" "=(6-4i^(2))/(1-4i^(2))`
`" "=(6+4)/(1+4)=(10)/(5)=2`
which is a real number. `" "` Hence proved.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN|Exercise EXERCISE 5A|9 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN|Exercise EXERCISE 5B|28 Videos

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN|Exercise Example|68 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|8 Videos

Similar Questions

Explore conceptually related problems

(1+2i)/(1+3i) is equal to

If (sqrt(3)+i)/(2)=(a+i)/(a-i) and a is a real number, then a is

Prove that: (i) [((3+2i)/(2-5i))+((3-2i)/(2+5i))] is rational (ii) [((2-3i)/(3-4i))((2+3i)/(3+4i))] is real.

((1+2i)^(3))/((1+i)(2-i))

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

If (3+2i sin theta)/(1-2i sin theta) is a real number and 0

If (3+2i sin theta)/(1-2i sin theta) is a real number and 0

(-i)(2i)(-(1)/(8)i)^(3)

Prove that z=i^(i), where i=sqrt(-1), is purely real.

NAGEEN PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATION -MISCELLANEOUS EXERCISE
  1. Prove that (3+i)/(1+2i)+(3-i)/(1-2i) is a real number.

    Text Solution

    |

  2. Evaluate : [i^(18)+(1/i)^(25)]^3

    Text Solution

    |

  3. Prove that Re (z1 z2)= Re z1 Re z2 - Imz1 Imz2 ,

    Text Solution

    |

  4. Reduce (1/(1-4i)-2/(1+i))((3-4i)/(5+i))to the standard form.

    Text Solution

    |

  5. If (a+i b)/(c+i d)=x+i y , prove that (a-i b)/(c-i d)=x-i ya n d(a^2+b...

    Text Solution

    |

  6. Convert the following in the polar form : (i) (1+7i)/((2-i)^2) (ii) (...

    Text Solution

    |

  7. Solve the equation : 3x^2-4x+(20)/3=0

    Text Solution

    |

  8. x^(2)-2x+(3)/(2)=0

    Text Solution

    |

  9. Solve the equation :27 x^2-10 x+1=0

    Text Solution

    |

  10. Solve the following quadratic: 21 x^2-28 x+10=0

    Text Solution

    |

  11. If z1=2-i ,z2=1+i ,find |(z1+z2+1)/(z1-z2+i)|

    Text Solution

    |

  12. If a + i b =((x+i)^2)/(2x^2+1),prove that a^2+b^2=((x^2+1)^2)/((2x^2+...

    Text Solution

    |

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

    Text Solution

    |

  14. Find the modulus and argument of the complex number (1+2i)/(1-3i).

    Text Solution

    |

  15. Find the real numbers x\ a n d\ y , if (x-i y)(3+5i) is the conjugate ...

    Text Solution

    |

  16. Find the modulus of (1+i)/(1-i)-(1-i)/(1+i).

    Text Solution

    |

  17. If (x+i y)^3=u+i v ,then show that u/x+v/y=4(x^2-y^2).

    Text Solution

    |

  18. If alpha and beta are different complex number with |beta|=1, then f...

    Text Solution

    |

  19. Find the number of non-zero integral solutions of the equation |1-i|^...

    Text Solution

    |

  20. If (a + i b) (c + i d) (e + i f) (g + i h) = A + i B, then show that (...

    Text Solution

    |

  21. If ((1+i)/(1-i))^m=1, then find the least positive integral value of m...

    Text Solution

    |