Home
Class 12
MATHS
For positive integer n1,n2 the value of ...

For positive integer `n_1,n_2` the value of the expression `(1+i)^(n1) +(1+i^3)^(n1) (1+i^5)^(n2) (1+i^7)^(n_20),` where `i=sqrt-1,` is a real number if and only if (a) `n_1=n_2+1` (b) `n_1=n_2-1` (c) `n_1=n_2` (d) `n_1 > 0, n_2 > 0`

A

`n_1=n_2 +1`

B

`n_1 = n_2 -1`

C

`n_1 = n_2`

D

`n_1 gt 0, n_2 gt 0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - II|22 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise COMPREHENSION - I|3 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - II|10 Videos

  • CIRCLE

    FIITJEE|Exercise Numerical Based|2 Videos

  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

For a positive integer n, find the value of (1-i)^(n)(1-(1)/(i))^(n)

The expression (1+i)^(n_1)+(1+i^(3))^(n_(2)) is real iff

The expression ((1+i)^(n))/((1-i)^(n-2)) equals

The value of i^(2n)+i^(2n+1)+i^(2n+2)+i^(2n+3), where i=sqrt(-1), is

If n_(1),n_(2) are positive integers,then (1+i)^(n_(1))+(1+i^(3))^(n_(1))+(1+i_(5))^(n_(2))+(1+i^(7))^(n_(2)) is real if and only if :

Find the integral values of n for the equations : (a) (1+i)^(n)=(1-i)^(n) (b) (1-i)^(n)=2^(n)

If n is any positive integer,write the value of (i^(4n+1)-i^(4n-1))/(2)

FIITJEE-COMPLEX NUMBER-ASSIGNMENT PROBLEMS (OBJECTIVE) Level - I
  1. A complex number z with (Im)(z)=4 and a positive integer n be such tha...

    Text Solution

    |

  2. For complex number z, the minimum value of |z| + |Z- cos alpha-I sin a...

    Text Solution

    |

  3. Equation of tangent drawn to circle abs(z)=r at the point A(z(0)), is

    Text Solution

    |

  4. Delta ABC be a triangle inscribed in a circle |z|=1 when B(Z1), C(Z2) ...

    Text Solution

    |

  5. If tangent at Z1, Z2 on the circle |Z- Z0|=r intersect at Z3. Then((Z3...

    Text Solution

    |

  6. If |(z-z1)/(z-z2)|=1, where z1 and z2 are fixed complex numbers and z ...

    Text Solution

    |

  7. Let arg(z(k))=((2k+1)pi)/(n) where k=1,2,………n. If arg(z(1),z(2),z(3),…...

    Text Solution

    |

  8. If ,Z1,Z2,Z3,........Z(n-1) are n^(th) roots of unity then the value ...

    Text Solution

    |

  9. For positive integer n1,n2 the value of the expression (1+i)^(n1) +(1+...

    Text Solution

    |

  10. If z1 , z2, z3 are complex numbers such that |z1|= |z2| = |z3|= |(1)/(...

    Text Solution

    |

  11. If |z+(2)/(z)|=2 then the maximum value of |z| is

    Text Solution

    |

  12. If . ( tan theta + (sin. (theta)/(2) +cos. (theta)/(2)))/(1+2i sin. (t...

    Text Solution

    |

  13. If a, b in C and z is a non zero complex number then the root of the e...

    Text Solution

    |

  14. If the ratio (1-z)/(1+z) is purely imaginary, then

    Text Solution

    |

  15. If z1 and z2 are two distinct non-zero complex number such that |z1|= ...

    Text Solution

    |

  16. If |z1|=1, |z2| = 2, |z3|=3 and |9z1 z2 + 4z1 z3+ z2 z3|=12, then the ...

    Text Solution

    |

  17. If z1, z2 and z3 be the vertices of Delta ABC, taken in anti-clock wi...

    Text Solution

    |

  18. If the point A1, A2,….,A8 be the affixes of the roots of the equation...

    Text Solution

    |

  19. Statement - 1 : If for any complex number z, |z-2|+|z-3|=4, then are ...

    Text Solution

    |

  20. Statement - 1: consider an ellipse with foci at A(z1) and B(z2) in the...

    Text Solution

    |