Home
Class 11
MATHS
If z=((sqrt(3))/2+i/2)^5+((sqrt(3))/2-i/...

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

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

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

If z=[(sqrt(3)/2)+i/2]^5+[((sqrt(3))/2)-i/2]^5 , then a. R e(z)=0 b. I m(z)=0 c. R e(z)>0 d. R e(z)>0,I m(z)<0

If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5 , then (a) im(z)=0 (b) Re(z)gt0 , Im(z)gt0 (c) Re(z)gt0 , Im(z)lt0 (d) Re(z)=3

If z= ((sqrt3)/(2) + (i)/(2))^(107) + ((sqrt3)/(2)-(i)/(2))^(107) , then show that Im(z)=0

If z(2-2sqrt(3i))^2=i(sqrt(3)+i)^4, then a r g(z)=

If z=i log(2-sqrt(3)) then cosz

For z_(1)=""^(6)sqrt((1-i)//(1+isqrt(3))),z_(2)=""^(6)sqrt((1-i)//(sqrt(3)+i)) , z_(3)= ""^(6)sqrt((1+i) //(sqrt(3)-i)) , prove that |z_(1)|=|z_(2)|=|z_(3)|

If z = (-4 +2 sqrt3i)/(5 +sqrt3i) , then the value of arg(z) is

if z = (sqrt 3 ) /(2) + (i)/(2) ( i=sqrt ( -1) ) , then ( 1 + iz + z^5 + iz^8)^9 is equal to:

If z=(1)/(2)(sqrt(3)-i) , then the least possible integral value of m such that (z^(101)+i^(109))^(106)=z^(m+1) is

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If det|6i -3i 1 4 3i-1 20 3 i|=x+i y , then a.x=3,y=1 b. x=1...

    Text Solution

    |

  2. Let z=x+i y be a complex number, where xa n dy are real numbers. Let...

    Text Solution

    |

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

    Text Solution

    |

  4. The value of sum(n=1)^(13) (i^n+i^(n+1)), where i =sqrt(-1) equals (...

    Text Solution

    |

  5. If c!=0 and the equation p//(2x)=a//(x+c)+b//(x-c) has two equal roo...

    Text Solution

    |

  6. If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a r...

    Text Solution

    |

  7. Express the following in a+i b form: ((cos2theta-isin2theta)^4(cos4...

    Text Solution

    |

  8. The roots of the equation t^3+3a t^2+3b t+c=0a r ez1, z2, z3 which rep...

    Text Solution

    |

  9. Solve the equation (x-1)^3+8=0 in the set C of all complex numbers.

    Text Solution

    |

  10. If 'z, lies on the circle |z-2i|=2sqrt2, then the value of arg((z...

    Text Solution

    |

  11. If the equation whose roots are the squares of the roots of the cubic ...

    Text Solution

    |

  12. If sqrt(3)+i=(a+i b)(c+i d) , then find the value of tan^(-1)(b//a)+ta...

    Text Solution

    |

  13. P(z) be a variable point in the Argand plane such that |z|=minimum {|z...

    Text Solution

    |

  14. If the equation a x^2+b x+c=0,a ,b ,c , in R have none-real roots, t...

    Text Solution

    |

  15. Prove that the equation Z^3+i Z-1=0 has no real roots.

    Text Solution

    |

  16. The locus of point z satisfying R e(1/z)=k , where k is a non zero re...

    Text Solution

    |

  17. If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p...

    Text Solution

    |

  18. Find the square root 9+40 idot

    Text Solution

    |

  19. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic e...

    Text Solution

    |

  20. Let a be a complex number such that |a|<1a n dz1, z2,z3,... be the ve...

    Text Solution

    |