Home
Class 11
MATHS
If (costheta-isintheta)^2 = x -iy, show ...

If `(costheta-isintheta)^2 = x -iy`, show that `x^2+y^2 = 1`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    A N EXCEL PUBLICATION|Exercise QUESTION BANK |106 Videos

  • CONIC SECTION

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|90 Videos

Similar Questions

Explore conceptually related problems

Prove that abs(costheta-isintheta) = 1

If x=2costheta , y=3sintheta Find dy/dx .

If (x+iy)^3 = u + iv , then show that u/x+v/y=4(x^2-y^2)

If x=sint and y=sinmt show that (1-x^2)y_2-xy_1+m^2y=0

If y=(tan^(-1)x)^2 , show that (x^2+1)^2y_2+2x(x^2+1)y_1=2 .

If arg((z-1)/(z+1)) = pi/2 , show that x^2+y^2-1=0

If y=e^(acos^-1x) , then show that (1-x^2)y_2-xy_1-a^2y=0

Given that logy=tan^-1x . Show that (1+x^2)y_1=y .

If cos ^-1 x+cos ^(-1) y+cos ^(-1) z=pi and 0ltx, y ,zlt1 ,show that x^2+y^2+z^2+2 x y z=1

If y=3 cos (log x)+4 sin (log x) Show that x^2 y_2+x y_1+y=0

A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. If a+ib = sqrt((1+i)/(1-i)), prove that a^2+b^2=1

    Text Solution

    |

  2. Prove that abs(costheta-isintheta) = 1

    Text Solution

    |

  3. If (costheta-isintheta)^2 = x -iy, show that x^2+y^2 = 1

    Text Solution

    |

  4. Complete the following table

    Text Solution

    |

  5. When two complex numbers are equal? Find the real values of x and y fo...

    Text Solution

    |

  6. Match the following

    Text Solution

    |

  7. Fill in the blanks by choosing the correct answer from the bracket ove...

    Text Solution

    |

  8. Suppose z1 = 1 - i and z2 = -2 + 4i Find z1z2

    Text Solution

    |

  9. Suppose z1 = 1 - i and z2 = -2 + 4i Find overlinez1

    Text Solution

    |

  10. Suppose z1 = 1 - i and z2 = -2 + 4i Find Im ((z1z2)/z1) and Re ((z1z2...

    Text Solution

    |

  11. Suppose z1 = 1 - i and z2 = -2 + 4i Joseph evaluted abs((z1z2)/z1) usi...

    Text Solution

    |

  12. Suppose z = x + iy and w = (1-iz)/(z-i) Find 1 - iz and z - 1 in the s...

    Text Solution

    |

  13. Suppose z = x + iy and w = (1-iz)/(z-i) Find absw. If absw = 1, prove...

    Text Solution

    |

  14. Consider the complex number z1 = 2 - i and z2 = -2 + i Find (z1z2)/z1...

    Text Solution

    |

  15. Consider the complex number z1 = 2 - i and z1 = -2 + i Raju prove tha...

    Text Solution

    |

  16. Consider the complex number z1 = 2 - i and z2 = 2 + i Find 1/(z1z2). ...

    Text Solution

    |

  17. Given that for any complex number z, absz^2 = zoverlinez . Prove that ...

    Text Solution

    |

  18. Given that for any complex number z, absz^2 = zoverlinez . Prove that ...

    Text Solution

    |

  19. Represent the following complex numbers as points in the argand plane ...

    Text Solution

    |

  20. Represent the following complex numbers as points in the argand plane ...

    Text Solution

    |