Home
Class 11
MATHS
Which of the following is true for z=(3...

Which of the following is true for `z=(3+2isintheta)(1-2sintheta)w h e r ei=sqrt(-1)` ? (a) z is purely real for `theta=npi+-pi/3,n in Z` (b)z is purely imaginary for `theta=npi+-pi/2,n in Z` (c) z is purely real for `theta=npi,n in Z` (d) none of these

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If (z-1)/(z+1) is purely imaginary then

Consider the complex number z=(1-isin theta)/(1+icos theta) The value of theta for nuber z is purely real is

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

Consider the complex number z=(1-isin theta)/(1+isin theta) The value of theta for which z is purely imagianry is

The straight line xcostheta+ysintheta=2 will touch the circle x^2+y^2-2x=0 if (a) theta=npi,n in I Q (b) A=(2n+1)pi,n in I (c) theta=2npi,n in I (d) none of these

If sintheta=1/2a n dcostheta=-(sqrt(3))/2, then the general value of theta is (n in Z)dot

If z is a complex number such that (z-1)/(z+1) is purely imaginary, then the value of |z| is-

Consider the complex number z=(1-isin theta)/(1+icos theta) If argument of z is (pi)/(4) , then

If z=x+iy and |z|=1 , show that (z-1)/(z+1)(z!=-1) is a purely imaginary quantity.

If z=x+iyand(z-i)/(z+1) is purely imaginary, then show that the point z always lies on a circle.

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Minimum value of (sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha), w...

    Text Solution

    |

  2. A man observes that when he moves up a distance c metres on a slope, ...

    Text Solution

    |

  3. Which of the following is true for z=(3+2isintheta)(1-2sintheta)w h e...

    Text Solution

    |

  4. Express 45^0 20 ' 10 ' ' in radian measure (pi=3. 1415)

    Text Solution

    |

  5. The number of solution of sec^2theta+cos e c^2theta+2cos e c^2theta=8,...

    Text Solution

    |

  6. The base of a triangle is divided into three equal parts. If t1, t2,t3...

    Text Solution

    |

  7. A man observes when he has climbed up 1/3 of the length of an inclined...

    Text Solution

    |

  8. Number of solutions of the equation sin^4x-cos^2xsinx+2sin^2x+sinx=0in...

    Text Solution

    |

  9. If the median AD of triangle ABC makes an angle pi/4 with the side BC,...

    Text Solution

    |

  10. If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4thet...

    Text Solution

    |

  11. The value of k if the equation 2 cos x + cos 2kx=3 has only one soluti...

    Text Solution

    |

  12. If I1, I2, I3 are the centers of escribed circles of triangle A B C ,...

    Text Solution

    |

  13. Let f(theta)=1/(1+(cottheta)^2) , and S=sum(theta=1^0)^(89^0)f(theta),...

    Text Solution

    |

  14. The number of values of theta in the interval (-pi/2,pi/2) satisfying ...

    Text Solution

    |

  15. If the distance between incenter and one of the excenter of an equi...

    Text Solution

    |

  16. The value of 3(sin^4t+cos^4t-1)/(sin^6t+cos^6t-1) is equal to

    Text Solution

    |

  17. Number of roots of the equation 2^(tan(x-pi/4))-2(0. 25)^((sin^2(x-pi...

    Text Solution

    |

  18. If sintheta-costheta=1, then the value of sin^3theta-cos^3theta is

    Text Solution

    |

  19. Given a triangle A B C with sides a=7, b=8 and c=5. Find the value of ...

    Text Solution

    |

  20. The smallest positive value of x (in radians) satisfying the equation...

    Text Solution

    |