Home
Class 11
MATHS
If x + i y =(a+i b)/(a-i b),prove that x...

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

Text Solution

Verified by Experts

The correct Answer is:
N/a
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISE 5C|14 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISE 5D|6 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISE 5A|9 Videos

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exericse|20 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|8 Videos

Similar Questions

Explore conceptually related problems

If x - i y =sqrt((a-i b)/(c-i d)) prove that x^2+y^2=(a^2+b^2)/(c^2+d^2)

If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d^2)

If x+i y=sqrt((a+i b)/(c+i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d^2)

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

If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

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

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

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

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

If x+i y=sqrt((a+i b)/(c+i d)), then write the value of (x^2+y^2)^2 .

NAGEEN PRAKASHAN ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATION -EXERCISE 5B
  1. Write the following in the form of ordered pair : (i) 3-2i (ii)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. The complex number z is purely imaginary , if

    Text Solution

    |

  12. A number of the form a + ib is called a complex number, where a,b in R...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. If (1+x)/(1 -x)=cos2theta +isin2theta, prove that that x=itantheta.

    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

    |