Home
Class 11
MATHS
Prove that abs((a+i)^2/(2a-i)) = (a^2+1)...

Prove that `abs((a+i)^2/(2a-i)) = (a^2+1)/(sqrt(4a^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((1+i)/(1-i)) = 1

Prove that (1 + i)^4 = -4

prove that (-1 + i)^2 = -2i

Prove that (1+i)^4(1+1/i)^4=16

If (a+i)^2/(2a-i) = p+iq , prove that p^2+q^2 = (a^2+1)^2/(4a^2+1)

Prove that tan ^(-1) ((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))=pi/4+1/2 cos ^(-1) x^2

Prove that sin[2tan^(-1){sqrt((1-x)/(1+x))}]=sqrt(1-x^2)

Prove that costan^(-1)sin cot^(-1)x=sqrt((x^2+1)/(x^2+2))

Prove that 2 tan ^(-1) (1/5)+sec ^(-1) ((5 sqrt2)/7)+2 tan ^(-1) (1/8)=pi/4

Find the value of (a^2+sqrt(a^2-1))^4+(a^2-sqrt(a^2-1))^4

A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Consider the complex number z1 = 3+i and z2 = 1+i .Find 1/z2

    Text Solution

    |

  2. Consider the complex number z1 = 3+i and z2 = 1+i .Using the value of ...

    Text Solution

    |

  3. Prove that abs((a+i)^2/(2a-i)) = (a^2+1)/(sqrt(4a^2+1))

    Text Solution

    |

  4. If (a+i)^2/(2a-i) = p+iq, prove that p^2+q^2 = (a^2+1)^2/(4a^2+1)

    Text Solution

    |

  5. If x=(1+i)/sqrt2, prove that x^2 = i

    Text Solution

    |

  6. If x=(1+i)/sqrt2.Prove that x^6+x^4+x^2+1=0

    Text Solution

    |

  7. Prove that abs((1+i)/(1-i)) = 1

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Complete the following table

    Text Solution

    |

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

    Text Solution

    |

  13. Match the following

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |