Home
Class 11
MATHS
Prove that (1+i)^n+(1-i)^n=2^((n+2)/2)....

Prove that ` (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4)`, where n is a positive integer.

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

(-i)^(4n+3) , where n Is a positive integer.

If A= [(3 , -4), (1 , -1) ] , then prove that A^n=[(1+2n , -4n), (n , 1-2n) ] , where n is any positive integer.

Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

Prove that sum_(k=1)^(n-1)(n-k)cos(2kpi)/n=-n/2 , where ngeq3 is an integer

The equatin 2x = (2n +1)pi (1 - cos x) , (where n is a positive integer)

Using permutation or otherwise, prove that (n^2)!/(n!)^n is an integer, where n is a positive integer. (JEE-2004]

Prove that ^n C_0+^n C_3+^n C_6+=1/3(2^n+2cos((npi)/3)) .

By using binomial theorem prove that (2^(3n)-7n-1) is divisible by 49 where n is a positive integer.

Show that int_0^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive integer and , 0<=vltpi

Show that int_0^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive integer and , 0<=vltpi

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamm...

    Text Solution

    |

  2. If x+y+z=12 andx^2+y^2+z^2=96 and 1/x+1/y+1/z=36 , then the value x^3+...

    Text Solution

    |

  3. Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4), where n is a pos...

    Text Solution

    |

  4. The set {R e((2i z)/(1-z^2)): zi sacom p l e xnu m b e r ,|z|=1,z=+-1}...

    Text Solution

    |

  5. If the equation x^2+ax+bc=0" and " x^2-bx+ca=0 have a common root, the...

    Text Solution

    |

  6. If a r g["z"1("z"3-"z"2)]="a r g"["z"3("z"2-"z"1)] , then find prove t...

    Text Solution

    |

  7. If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2...

    Text Solution

    |

  8. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) , then c is equ...

    Text Solution

    |

  9. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

    Text Solution

    |

  10. If z=(a+ib)^5+(b+ia)^5 then prove that Re(z)=Im(z), where a,b in R.

    Text Solution

    |

  11. If a and b are positive numbers and eah of the equations x^2+a x+2b=0 ...

    Text Solution

    |

  12. The real values of xa n dy for which the following equation is satisfi...

    Text Solution

    |

  13. The three angular points of a triangle are given by Z=alpha, Z=beta,Z=...

    Text Solution

    |

  14. Suppose a ,b ,c are the roots of the cubic x^3-x^2-2=0. Then the value...

    Text Solution

    |

  15. Prove that x^3 + x^2 + x is factor of (x+1)^n - x^n -1 where n is odd ...

    Text Solution

    |

  16. If alpha,beta,gamma,delta are four complex numbers such that gamma/del...

    Text Solution

    |

  17. If ax^(2)+(b-c)x+a-b-c=0 has unequal real roots for all c epsilonR, th...

    Text Solution

    |

  18. If z1^2+z2^2-2z1.z2.costheta= 0 prove that the points represented by ...

    Text Solution

    |

  19. Prove that the circles z bar z +z( bar a 1)+bar z( a1 )+b1=0 ,b1 in ...

    Text Solution

    |

  20. If a , b ,c real in G.P., then the roots of the equation a x^2+b x+c=0...

    Text Solution

    |