Home
Class 12
MATHS
Express each of the following expression...

Express each of the following expressions as the sum of two squares: `(1+x^(2))(1+y^(2))`

Text Solution

Verified by Experts

The correct Answer is:
`(1-xy)^(2)+(x+y)^(2)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVEEXAMS(Multiple Corrrect Answer type)|7 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVE EXAMS(Multiple Corrrect Answer type)|11 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise EXERCISE 4(SHORT ANSWER TYPE QUESTION )|58 Videos

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (E. Assertion-Reason Type)|2 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion - Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

Express each of the following expressions as the sum of two squares: (a^(2)+b^(2))(c^(2)+d^(2))

Let's express the expressions as sum of two squares: 2(a^2 + b^2)

Express each of the following quadratic equations as the difference of two squares and solve x^2+x+1=0

Express each of the following quadratic equations as the difference of two squares and solve x^2+1=0

Express each of the following quadratic equations as the difference of two squares and solve 2x^2+2x+5=0

Express each of the following quadratic equations as the difference of two squares and solve 3x^2-2x+2=0

Express each of the following quadratic equations as the difference of two squares and solve 8x^2+4x+13=0

Express each of the following quadratic equations as the difference of two squares and solve 9x^2+12x+10=0

Express each of the following quadratic equations as the difference of two squares and solve 5x^2-6x+5=0

Express each of the following quadratic equations as the difference of two squares and solve 9x^2+16=0

CHHAYA PUBLICATION-COMPLEX NUMBER-EXERCISE 4(LONG ANSWER TYPE QUESTION )
  1. If x,y,b and real, z=x+iy and (z-i)/(z-1)=ib, show that, (x-(1)/(2))...

    Text Solution

    |

  2. If x+iy=(2)/(3+cos theta+isin theta),"show that" " " 2x^(2)+2y^(2)=3x-...

    Text Solution

    |

  3. If y=sqrt(x^(2)+6x+8), show that one value of sqrt(1+iy)+sqrt(1-iy)[i...

    Text Solution

    |

  4. Factorise : x^(2)+y^(2)+z^(2)-xy-yz-zx

    Text Solution

    |

  5. prove that , (a+bomega+comega^(2))^(3)+(a+bomega^(2)+comega)^(3)=27abc...

    Text Solution

    |

  6. Express each of the following expressions as the sum of two squares: (...

    Text Solution

    |

  7. Express each of the following expressions as the sum of two squares: ...

    Text Solution

    |

  8. Express each of the following expressions as the sum of two squares: (...

    Text Solution

    |

  9. If a,b are real and a^(2)+b^(2)=1 then show that the equation (sqrt(1...

    Text Solution

    |

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

    Text Solution

    |

  11. If z(1)and z(2) be any two non-zero complex numbers such that |z(1)+z(...

    Text Solution

    |

  12. If alpha be the real positive cube root and beta,gamma be the complex ...

    Text Solution

    |

  13. If arg""(z-1)/(z+1)=(pi)/(4), show that the locus of z in the complex ...

    Text Solution

    |

  14. In the complex plane, the vertices of an equlitateral triangle are rep...

    Text Solution

    |

  15. Show that the area of the triangle on the Argrand Diagram formed by th...

    Text Solution

    |

  16. If z(1)^(2)+z(2)^(2)+z(3)^(2)-z(1)z(3)-z(1)z(2)-z(2)z(3)=0" ""prove th...

    Text Solution

    |

  17. Solve bar(z)=iz^(2) (z being a complex number)

    Text Solution

    |

  18. Solve : |z|+z=2+i (z being a complex number)

    Text Solution

    |

  19. If z=x+iy then show that |x|+|y|lesqrt2|x+iy|.

    Text Solution

    |

  20. Let z=x+iy and omega=(1-iz)/(z-i). If |omega|=1 show the in the comple...

    Text Solution

    |