Home
Class 12
MATHS
If z(1+a)=b+i ca n da^2+b^2+c^2=1, then ...

If `z(1+a)=b+i ca n da^2+b^2+c^2=1,` then `[(1+i z)//(1-i z)=` `(a+i b)/(1+c)` b. `(b-i c)/(1+a)` c. `(a+i c)/(1+b)` d. none of these

A

`(a + ib)/(1 +c)`

B

`(a -ib)/(1 +c)`

C

`(a +ib)/(1-c)`

D

`(a-ib)/(1-c)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ML KHANNA|Exercise Problem Set (2) (True and False )|4 Videos
  • COMPLEX NUMBERS

    ML KHANNA|Exercise Problem Set (2) (Fill in the blanks)|2 Videos
  • COMPLEX NUMBERS

    ML KHANNA|Exercise Problem Set (1) (True and False)|5 Videos
  • CO-ORDINATE GEOMETRY OF THREE DIMENSION

    ML KHANNA|Exercise SELF ASSIGNMENT TEST |11 Videos
  • CONCEPTS OF SET THEORY

    ML KHANNA|Exercise Self Assessment Test|13 Videos

Similar Questions

Explore conceptually related problems

If z(1+a)=b+icanda^(2)+b^(2)+c^(2)=1 then [(1+iz)/(1-iz)=(a+ib)/(1+c) b.(b-ic)/(1+a)c(a+ic)/(1+b) d.none of these

If z=(1)/((2+3i)^(2)), then |z| is a.(1)/(13) b.(1)/(5) c.(1)/(12)d .non of these

If z=(1)/((1-i)(2+3i)), then |z| is a.1 b.(1)/(sqrt(26)) c.(5)/(sqrt(26))d .non of these

If z=(1+2i)/(1-(1-i)^(2)), then arg (z) equals a.0 b.(pi)/(2) c.pi d .non of these

If z=((1+i)/(1-i)), then z^(4) equals a.1b.-1c0d non of these

If a,b,c are real numbers and z is a complex number such that,a^(2)+b^(2)+c^(2)=1 and b+ic=(1+a)z then (1+iz)/(1-iz) equals.(a) (b-ic)/(1-ia) (b) (a+ib)/(1+c) (c) (1-c)/(a-ib)( d) (1+a)/(b+ic)

Roots of the equation are (z+1)^(5)=(z-1)^(5) are (a)+-i tan((pi)/(5)),+-i tan((2 pi)/(5))(b)+-i cot((pi)/(5)),+-i cot((2 pi)/(5))(c)+-i cot((pi)/(5)),+-i tan((2 pi)/(5))(d)none of these

If A^(3)=O, then I+A+A^(2) equals I-A b.(I+A^(1))=^(-1) c.(I-A)^(-1) d.none of these

The points A(z_1), B(z_2) and C(z_3) form an isosceles triangle in the Argand plane right angled at B, then (z_1-z_2)/(z_3-z_2) can be (A) 1 (B) -1 (C) -i (D) none of these

If a+b+c=1,a^(2)+b^(2)+c^(2)=9 and a^(3)+b^(3)+c^(3)=1, then (1)/(a)+(1)/(b)+(1)/(c) is (i)0 (ii) -1(iii)1(iv)3

ML KHANNA-COMPLEX NUMBERS -Problem Set (2) (M.C.Q)
  1. ((cos theta + i sin theta)^(4))/( (sin theta + i cos theta)^(5)) is eq...

    Text Solution

    |

  2. If a^(2)+b^(2)=1, prove that (1+b+ia)/(1+b-ia)=b+ia.

    Text Solution

    |

  3. If z(1+a)=b+i ca n da^2+b^2+c^2=1, then [(1+i z)//(1-i z)= (a+i b)/(1...

    Text Solution

    |

  4. The value of sum (k = 1)^(6) ( sin "" ( 2 pi k)/( 7) - i cos "" ( 2 p...

    Text Solution

    |

  5. The value of sum (k = 0) ^(10) ( sin "" ( 2 k pi)/(11) + i cos "" (2 ...

    Text Solution

    |

  6. [(1 + sin "" (pi)/( 8) + i cos "" (pi)/( 8))/( 1 + sin "" (pi)/( 8) - ...

    Text Solution

    |

  7. If [(1 + cos theta + i sin theta)/( sin theta + i (1 + cos theta))] ^...

    Text Solution

    |

  8. The value of 1 + sum (k = 0)^( 12) { cos "" (( 2 k + 1) pi)/( 13) + i...

    Text Solution

    |

  9. If z(r) = cos ( pi // 2^(r)) + i sin ( pi // 2 ^(r)) r = 1, 2, . . . ...

    Text Solution

    |

  10. If zr=cos(pi/(3r))+isin(pi/(3r)),r=1,2,3, , prove that z1z2z3 zoo=idot

    Text Solution

    |

  11. If z=ilog(e)(2-sqrt(3)),"where"i=sqrt(-1) then the cos z is equal to

    Text Solution

    |

  12. The value of (tan(i*log((a-ib)/(a+ib)))) is

    Text Solution

    |

  13. If x satisfies the equation x^(2) - 2 x cos theta + 1 = 0 then the ...

    Text Solution

    |

  14. If 2 cos theta = x + (1)/( x) , 2 cos phi = y + (1)/( y) then

    Text Solution

    |

  15. The equation whose roots are nth power of the roots of the equations...

    Text Solution

    |

  16. If x^(2) - 2 x cos theta + 1 = 0 " then " x^(2 n) - 2 x ^(n) cos n th...

    Text Solution

    |

  17. The following in the form A + i B ( cos 2 theta + i sin 2 theta )^(-...

    Text Solution

    |

  18. If x = cos theta + i sin theta , y = cos phi + i sin phi z = cos Ps...

    Text Solution

    |

  19. If a = cos alpha + i sin alpha , b = cos beta + i sin beta , " then ...

    Text Solution

    |

  20. If cos A + cos B + cos C = 0, sin A + sin B + sin C = 0 and A + B +...

    Text Solution

    |