Home
Class 12
MATHS
If z=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5...

If `z=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5` , then prove that `Im(z)=0`

A

R(z) `gt 0` and `I(z) gt 0`

B

`R(z) lt 0` and `I(z) gt 0`

C

`R(z) = -3`

D

I(z) = 0

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If z = ((sqrt(3))/(2) + (i)/(2))^(107) + ((sqrt(3))/(2)-(i)/(2))^(107) , then show that Im (z) = 0

Show that ((sqrt(3))/(2) + (i)/(2))^(5) + ((sqrt(3))/(2) - (i)/(2))^(5) = -sqrt(3)

If z=((sqrt(3)+i)^(3)(3i+ 4)^(2))/((8+6i)^(2)) , then |z| is equal to

A(z_1),B(z_2),C(z_3) are the vertices of the triangle A B C (in clockwise). If /_A B C=pi//4 and A B=sqrt(2)(B C) , then prove that z_2=z_3+i(z_1-z_3)dot

If z = ((sqrt(3) + i)^(3) (3i+4)^(2))/((8 + 6i)^(2)) , then |z| is equal to

If z=(-1)/(2)+i(sqrt(3))/(2), " then "8+10z+7z^(2) is equal to

If z!=0 is a complex number, then prove that R e(z)=0 rArr Im(z^2)=0.

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2

CENGAGE-JEE 2019-MCQ
  1. Let Z0 is the root of equation x^2+x+1=0 and Z=3+6i(Z0)^(81)-3i(Z0)^(9...

    Text Solution

    |

  2. Let z(1) and z(2) be any two non-zero complex numbers such that 3|z(1)...

    Text Solution

    |

  3. If z=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5 , then prove that Im(z)=0

    Text Solution

    |

  4. Let (-2 -1/3 i)^3=(x+iy)/27 (i= sqrt(-1)) where x and y are real numbe...

    Text Solution

    |

  5. Let (z-alpha)/(z+alpha) is purely imaginary and |z|=2, alphaepsilonR t...

    Text Solution

    |

  6. Let Z(1) and Z(2) be two complex numbers satisfying |Z(1)|=9 and |Z(2)...

    Text Solution

    |

  7. Consider the statement : " P(n) : n^(2)-n+41 is prime." Then, which on...

    Text Solution

    |

  8. If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , the...

    Text Solution

    |

  9. Let a(1), a(2),....a(3) be an AP, S = sum(i = 1)^(30) a(i) and T = su...

    Text Solution

    |

  10. The sum of series 1+6+(9(1^(2)+2^(2)+3^(2)))/(7) + (12(1^(2)+2^(2)+...

    Text Solution

    |

  11. Let a, b and c be the 7th, 11th and 13th terms, respectively, of a non...

    Text Solution

    |

  12. The sum of all two digit positive numbers which when divided by 7 yiel...

    Text Solution

    |

  13. If 5, 5r and 5r^(2) are the lengths of the sides of a triangle, then r...

    Text Solution

    |

  14. The sum of an infinite geometric series with positive terms is 3 and t...

    Text Solution

    |

  15. Let a1, a2, a3, ?a10 are in G.P. if a3/a1 =25 then a9/a5 is equal to ...

    Text Solution

    |

  16. If 19th term of a non-zero AP is zero, then its (49th term) : (29 th t...

    Text Solution

    |

  17. The product of three consecutive terms of a GP is 512. If 4 is added t...

    Text Solution

    |

  18. Let S(k) = (1+2+3+...+k)/(k). If S(1)^(2) + s(2)^(2) +...+S(10)^(2) = ...

    Text Solution

    |

  19. If the sum of the first 15 terms of the series ((3)/(4))^(3)+(1(1)/(2)...

    Text Solution

    |

  20. Let x, y be positive real numbers and m, n be positive integers, The ...

    Text Solution

    |