Home
Class 11
MATHS
If n1, n2 are positive integers, then (1...

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 :

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

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

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

If n is an odd integer, then (1 + i)^(6n) + (1-i)^(6n) is equal to

If n ge 1 is a positive integer, then prove that 3^(n) ge 2^(n) + n . 6^((n - 1)/(2))

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

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

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

The last positive integer n for which ((1+i)/(1-i))^(n) is real, is

What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n)?

What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n) ?

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let z and omega be two complex numbers such that |z|lt=1,|omega|lt=1 ...

    Text Solution

    |

  2. Consider the equation x^2+2x-n=0 where n in N and n in [5,100] The t...

    Text Solution

    |

  3. If n1, n2 are positive integers, then (1 + i)^(n1) + ( 1 + i^3)^(n1) +...

    Text Solution

    |

  4. The total number of values a so that x^2-x-a=0 has integral roots, wh...

    Text Solution

    |

  5. If i=sqrt-1, then 4+5(-1/2+(isqrt3)/2)^334+3(-1/2+(isqrt3)/2)^365 is e...

    Text Solution

    |

  6. Let P(x)=x^3-8x^2+c x-d be a polynomial with real coefficients and wi...

    Text Solution

    |

  7. If a r g(z)<0, then a r g(-z)-"a r g"(z) equals pi (b) -pi (d) -pi/2...

    Text Solution

    |

  8. Let P(x)=5/3-6x-9x^2a n dQ(y)=-4y^2+4y+(13)/2dot if there exists uniq...

    Text Solution

    |

  9. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

    Text Solution

    |

  10. if a lt c lt b, then check the nature of roots of the equation (a ...

    Text Solution

    |

  11. Q. Let z1 and z2 be nth roots of unity which subtend a right angle at...

    Text Solution

    |

  12. If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+...

    Text Solution

    |

  13. The complex numbers z1, z2 and z3 satisfying (z1-z3)/(z2-z3) =(1- i sq...

    Text Solution

    |

  14. Find the value of a for which the sum of the squares of the roots of t...

    Text Solution

    |

  15. For all complex numbers z1,z2 satisfying |z1|=12 and |z2-3-4i|=5, fin...

    Text Solution

    |

  16. If x1, a n dx2 are the roots of x^2+(sintheta-1)x-1/2(cos^2theta)=0, ...

    Text Solution

    |

  17. If y="sec"(tan^(-1)x),t h e n(dy)/(dx)a tx=1 is (a)cospi/4 (b) sinp...

    Text Solution

    |

  18. If p ,q in {1,2,3,4,5} , then find the number of equations of form p^2...

    Text Solution

    |

  19. If a^2+b^2=1 t h e n (1+b+i a)/(1+b-i a)= 1 b. 2 c. b+i a d. a+...

    Text Solution

    |

  20. Find the domain and the range of f(x)=sqrt(x^2-3x.)

    Text Solution

    |