Home
Class 11
MATHS
Find the real values of theta for which ...

Find the real values of `theta` for which the complex number `(1+i costheta)/(1-2i costheta)` is purely real.

Text Solution

Verified by Experts

The correct Answer is:
N/a
`(2n+1)(pi)/(2), n in I`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN|Exercise EXERCISE 5C|14 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN|Exercise EXERCISE 5D|6 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN|Exercise EXERCISE 5A|9 Videos

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN|Exercise Example|68 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|8 Videos

Similar Questions

Explore conceptually related problems

Find the real values of theta for which the complex number (1+i cos theta)/(1-2i cos theta) is purely real.

The real value of theta for which the expression (1+i cos theta)/(1-2i cos theta) is real number is

The real value of theta for which the expression (1 + icos theta)/(1 - 2i cos theta) is real number is

The real value of alpha for which the expression (1-i sin alpha)/(1+2i sin alpha) is purely real is

Find real theta such that (3+2i sin theta)/(1-2i sin theta) is purely real.

Evaluate sqrt((1-cos theta)/(1+costheta))

NAGEEN PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATION -EXERCISE 5B
  1. Find the multiplicative inverse of the following complex number: (2+sq...

    Text Solution

    |

  2. Write the following in the form of ordered pair : (i) 3-2i (ii)...

    Text Solution

    |

  3. Convert the following in the form of a complex number : (i) (2, -5)...

    Text Solution

    |

  4. Find the values of x and y from the following : (i) (3x -7)+2iy=-5y+...

    Text Solution

    |

  5. If z=1+2i, show that z^(2)-2z+5=0. Hence find the value of z^(3) +7z^...

    Text Solution

    |

  6. Z=-5+4i then Z^4 +9Z^3 +35Z^2 – Z + 4 =

    Text Solution

    |

  7. If z(1)=2-i, z(2)=1+ 2i, then find the value of the following : (i)...

    Text Solution

    |

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

    Text Solution

    |

  9. (x+iy)^(1/3) =(a+ib) then prove that (x/a+y/b)=4(a^2-b^2)

    Text Solution

    |

  10. If = (a^(2) + 1)^(2)/(2a-i)=x+iy," then when is the value of " x^(2)+...

    Text Solution

    |

  11. Write the least positive integral value of n for which ((1+i)/(1-i))^n...

    Text Solution

    |

  12. The complex number z is purely imaginary , if

    Text Solution

    |

  13. If a^2+b^2=1.Then (1+b+ia)/(1+b-ia)=

    Text Solution

    |

  14. Find the real values of theta for which the complex number (1+i costhe...

    Text Solution

    |

  15. Find the square root of the following : (i) 3-4i (ii) 4+6isqrt(5) ...

    Text Solution

    |

  16. If x+iy=3/(2+costheta +i sin theta), then show that x^2+y^2=4x-3

    Text Solution

    |

  17. The sum and product of two complex numbers are real if and only if the...

    Text Solution

    |

  18. If x= cos alpha+ i sin alpha, y = cos beta+ i sin beta, then prove th...

    Text Solution

    |

  19. Prove that: x^4=4=(x+1+i)(x+1-i)(x-1+i(x-1-i)dot)

    Text Solution

    |

  20. Evaluate : (4+3sqrt(-20))^(1//2)+(4-3 sqrt(-20))^(1//2)

    Text Solution

    |