Home
Class 12
MATHS
Dividing f(z) by z-i, we obtain the rema...

Dividing f(z) by z-i, we obtain the remainder 1-i and dividing it by z+i, we get the remainder 1+i. Then, the remainder upon the division of f(z) by `z^(2)+1`, is

A

i+z

B

1+z

C

1-z

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos
  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Passage Based Questions)|12 Videos
  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 4|14 Videos
  • CIRCLE

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

Similar Questions

Explore conceptually related problems

Dividing f(z) by z- i , we obtain the remainder i and dividing it by z + i , we get the remainder 1 + i, then remainder upon the division of f(z) by z^2+1 is

If z=1+i, then what is the inverse of z^(2) ?

If the remainders respectively when f(z) = z^(3)+z^(2)+2z+1 is divided with z-i and z+i are 1+3i and 1+i then find the remainder when f(z) is divided with z^(2)+1 ?

When x is divided by 3 remainder is z.In terms of z, which of the following could be equal to x?

If z=(1+i tan alpha)^(1+i) , then find the magnitude of Z.

x=20, y=32 and z=12 {:("Quantity A","Quantity B"),("The remainder when x is","The remainder when y is "),("divided by z","divided by z"):}

If the polynomials az^3+4z^2+3z-4 and z^3-4z+a leave the same remainder when divided by z-3 , find the value of a.

if (1+i)z=(1-i)barz then z is

Find the radius and centre of the circle z bar(z) + (1-i) z + (1+ i) bar(z)- 7 = 0

The triangle with vertices at the point z_1z_2,(1-i)z_1+i z_2 is

ARIHANT MATHS ENGLISH-COMPLEX NUMBERS-Exercise (Single Option Correct Type Questions)
  1. If f(x)=g(x^(3))+xh(x^(3)) is divisiblel by x^(2)+x+1, then

    Text Solution

    |

  2. If the points represented by complex numbers z(1)=a+ib, z(2)=c+id " an...

    Text Solution

    |

  3. Let C and R denote the set of all complex numbers and all real numb...

    Text Solution

    |

  4. Let alpha and beta be two distinct complex numbers, such that abs(alph...

    Text Solution

    |

  5. The complex number z satisfies thc condition |z-25/z|=24. The maximum ...

    Text Solution

    |

  6. The points A,B and C represent the complex numbers z(1),z(2),(1-i)z(1)...

    Text Solution

    |

  7. The system of equations |z+1-i|=sqrt2 and |z| = 3 has how many soluti...

    Text Solution

    |

  8. Dividing f(z) by z-i, we obtain the remainder 1-i and dividing it by z...

    Text Solution

    |

  9. The centre of circle represented by |z + 1| = 2 |z - 1| in the complex...

    Text Solution

    |

  10. If x=9^(1/3) 9^(1/9) 9^(1/27) ......ad inf y= 4^(1/3) 4^(-1/9) 4^(1/...

    Text Solution

    |

  11. If center of a regular hexagon is at the origin and one of the vertice...

    Text Solution

    |

  12. Let |Z(r) - r| le r, Aar = 1,2,3….,n. Then |sum(r=1)^(n)z(r)| is less ...

    Text Solution

    |

  13. If arg ((z(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z(1)|...

    Text Solution

    |

  14. about to only mathematics

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. If z=(3+7i)(lambda+imu)," when " lambda,mu in I-{0} " and " i=sqrt(-1...

    Text Solution

    |

  17. Given z=f(x)+ig(x) where f,g:(0,1) to (0,1) are real valued functions....

    Text Solution

    |

  18. If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies...

    Text Solution

    |

  19. If m and n are the smallest positive integers satisfying the relation ...

    Text Solution

    |

  20. Number of imaginergy complex numbers satisfying the equation, z^(2)=ba...

    Text Solution

    |