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

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

Text Solution

Verified by Experts

The correct Answer is:
`(iz)/(2)+1/2+i`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -I) PREVIOUS YEAR - JEE MAIN|12 Videos

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED|33 Videos

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 2 (LEVEL -II) MULTIPLE CORRECT - JEE ADVANCED|10 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

Similar Questions

Explore conceptually related problems

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

On dividing a positive integers n by 9, we get 7 as remainder. What will be the remainder if ( 3n-1) is divided by 9 ?

A number divided by 13 leaves a remainder 1 and if the quotient, thus obtained, is divided by 5, we get a remainder of 3. What will be the remainder if the number is divided by 65? 16 (b) 18 (c) 28 (d) 40

When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5, the remainder is 4, The remainder is z when x+y is divided by 5. The value of (2z-5)/(3) is

Find the remainder when the polynomital p(z)=z^(3)-3z+2 is divided by z-2.

On dividing a number by 13, we get 1 as remainder. If the quotient is divided by 5. we get 3 as a remainder. If this number is divided by 65, what will be the remainder ?

| z | -z = 1 + 2i

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.

MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
  1. If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. ...

    Text Solution

    |

  2. If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. ...

    Text Solution

    |

  3. The region represented by RE(z)<=2, Im(z)<=2 and pi/8<=arg(z)<=(3pi)/8...

    Text Solution

    |

  4. Let I Arg((z-8i)/(z+6))=pmpi/2 II: Re ((z-8i)/(z+6))=0 Show that ...

    Text Solution

    |

  5. if a and bbetween 0 and 1 such that the points (a, 1). (1, b) and (0, ...

    Text Solution

    |

  6. Find the non-zero complex numbers z satisfying z =i z^2dot

    Text Solution

    |

  7. If the complex numbers z1, z2,.......zn lie on te unit circle |z| = 1 ...

    Text Solution

    |

  8. Find the Cartesian equations of the locus of z in the complex plane sa...

    Text Solution

    |

  9. Prove that the complex numbers z1 and z2 and the origin form an isosce...

    Text Solution

    |

  10. If the complex number P(w) lies on the standard unit circle in an Arg...

    Text Solution

    |

  11. Let z=x+i y be a complex number, where xa n dy are real numbers. Let A...

    Text Solution

    |

  12. For all real numbers x, let the mapping f (x) = 1/(x-i). where i =sqrt...

    Text Solution

    |

  13. Given that |z-1|=1, where z is a point on the argand planne , show...

    Text Solution

    |

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

    Text Solution

    |

  15. If the equation x^4+ax^3+bx^2+cx+d=0 has four imaginary roots two with...

    Text Solution

    |

  16. If z1, z2 are the roots of the equation az^2 + bz + c = 0, with a, b, ...

    Text Solution

    |

  17. Find the set of points on the argand plane for which the real part of ...

    Text Solution

    |

  18. The equation z^n – 1 = 0 has n roots which are called the nth roots o...

    Text Solution

    |

  19. The equation z^n – 1 = 0 has n roots which are called the nth roots o...

    Text Solution

    |

  20. MATCH THE COLUMN {:(Column-I,Column-II),("(A) If "|ai|lt1,lamda1ge0 ...

    Text Solution

    |