Home
Class 11
MATHS
If i=sqrt(-1) then 4+5(-1/2+(isqrt3)/2)^...

If `i=sqrt(-1)` then `4+5(-1/2+(isqrt3)/2)^334+3(-1/2+(isqrt3)/2)^365` is equal to

A

`1-isqrt3`

B

`(-1)+isqrt3`

C

`isqrt3`

D

`(-1)sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos
  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

Find the value of 4+5[-(1)/(2)-i(sqrt(3))/(2)]^(344)+3[-(1)/(2)+i(sqrt(3))/(2)]^(365) (i=sqrt(-1))

Find the amplitude of ((sqrt3+i)/(-1-isqrt3))

4 cos^(2)x + sqrt(3) = 2(sqrt(3)+1)

The sum of the series (1)/(sqrt1+sqrt2)+ (1)/(sqrt2+ sqrt3)+ ...+ (1)/(sqrt(n)+sqrt(n+1)) is equal to-

Simiplify (1)/(7+4sqrt3)+(1)/(2+sqrt5)

int (x^2 - 1)/((x^3)sqrt(2x^4- 2x^2 + 1)) dx is equal to

Show that 4sin27^0=(5+sqrt(5))^(1/2)+(3-sqrt(5))^(1/2)

If a , b ,c real in G.P., then the roots of the equation a x^2+b x+c=0 are in the ratio a. 1/2(-1+isqrt(3)) b. 1/2(1-isqrt(3)) c 1/2(-1-isqrt(3)) d. 1/2(1+isqrt(3))

If 3tan^(-1)(1/(2+sqrt(3)))-tan^(-1)(1/x)=tan^(-1)(1/3), then x is equal to 1 (b) 2 (c) 3 (d) sqrt(2)

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. if x=9^(1/3)9^(1/9)9^(1/27)…..infty,y=4^(1/3)4^(1/9)4^(1/27)…..infty a...

    Text Solution

    |

  2. If the fourth roots of unity are z1,z2,z3,z4 then z1^2+z2^2+z3^2+z4^2 ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. If x^5=(4-3i)^5 thrn the product of all of its roots (wheretheta=-tan^...

    Text Solution

    |

  6. If omega is an imaginary x^n root of unit then underset(r=1)oversetnsu...

    Text Solution

    |

  7. If omega(ne1) be a cube root of unity and (1+omega^2)^n=(1+omega^4)^n ...

    Text Solution

    |

  8. If absz=1 and z ne+-1 then all the values of z/(1-z^2) lie on

    Text Solution

    |

  9. If (1+2i)/(2+i)=r(costheta+isintheta) then

    Text Solution

    |

  10. If z1=a+ib and z2=c+id are two complex numbers lying on the circle x^...

    Text Solution

    |

  11. Number of solution(s) of the equation absz^2+7z=0 is/are

    Text Solution

    |

  12. If z1=9y^2-4-10ix,z2=8y^2-20i where z1=barz2 then z=x+iy is equal to

    Text Solution

    |

  13. Let z1,z2,z3 be three points on absz=1 let theta1,theta2 and theta3 be...

    Text Solution

    |

  14. If z1,z2 are two non zero complex numbers such that z1/z2+z2/z1=1 then...

    Text Solution

    |

  15. The complex numbers z1,z2 and z3 satisfying (z1-z3)/(z2-z3)=(1-isqrt3)...

    Text Solution

    |

  16. Let A(z1),A2(barz1) are the adjacent vertices of a regular polygon if ...

    Text Solution

    |

  17. If the points A(z),B(-z),C(1-z) are the vertices of an equilateral tri...

    Text Solution

    |

  18. Let z1 nez2 are two points in the Argand plane if a abs(z1)=b abs(z2) ...

    Text Solution

    |

  19. The least positive integer n for which ((1+i)/(1-i))^n=2/pisin^(-1)((1...

    Text Solution

    |

  20. If x=2+5i then the value of the expression x^3-5x^2+33x-49 is

    Text Solution

    |