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

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`

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 I m(z)=0.

If z=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5 , then prove that Im(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 = (-4 +2 sqrt3i)/(5 +sqrt3i) , then the value of arg(z) is

If z!=0 be a complex number and a rg(z)=pi/4, then R e(z)=I m(z)on l y R e(z)=I m(z)>0 R e(z^2)=I m(z^2) (d) None of these

If z=(a+i b)^5+(b+i a)^5 , then prove that R e(z)=I m(z),w h e r ea ,b in Rdot

If z=ilog_(e)(2-sqrt(3)),"where"i=sqrt(-1) then the cos z is equal to

Given z=(1+isqrt(3))^(100), then [R E(z)//I M(z)] equals 2^(100) b. 2^(50) c. 1/(sqrt(3)) d. sqrt(3)

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. |z-4| < |z-2| represents the region given by: (a) Re(z) > 0 (b) Re(z) ...

    Text Solution

    |

  2. Find how many roots of the equations x^4+2x^2-8x+3=0.

    Text Solution

    |

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

    Text Solution

    |

  4. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

    Text Solution

    |

  5. The complex numbers z=x+iy which satisfy the equation |(z-5i)/(z+5i)|=...

    Text Solution

    |

  6. Solve sqrt(5x^2-6x+8)-sqrt(5x^2-6x-7)=1.

    Text Solution

    |

  7. The smallest positive integer n for which ((1+i)/(1-i))^n=1 is (a)8...

    Text Solution

    |

  8. Solve sqrt(3x^2-7x-30)+sqrt(2x^2-7x-5)=x+5.

    Text Solution

    |

  9. If the cube roots of unity are 1,omega,omega^2, then the roots of the ...

    Text Solution

    |

  10. If x= (7+4sqrt(3)), prove that x+1//x= 14

    Text Solution

    |

  11. Prove that the locus of midpoint of line segment intercepted between ...

    Text Solution

    |

  12. Solve sqrt(5x^2-6x+8)-sqrt(5x^2-6x-7)=1.

    Text Solution

    |

  13. Show that: sum(r=0)^(n-1)|z1+alpha^r z2|^2=n(|z1|^2+|z2|^2),w h e r e,...

    Text Solution

    |

  14. Solve sqrt(x^2+4x-21)+sqrt(x^2-x-6)=sqrt(6x^2-5x-39.)

    Text Solution

    |

  15. If alpha=(z-i)(z+i), show that, when z lies above the real axis, alpha...

    Text Solution

    |

  16. Solve 4^x+6^x=9^xdot

    Text Solution

    |

  17. Let x1, x2 are the roots of the quadratic equation x^2+a x+b=0,w h e r...

    Text Solution

    |

  18. Solve 3^(2x^2-7x+7)=9.

    Text Solution

    |

  19. Plot the region represented by pi/3lt=a r g((z+1)/(z-1))lt=(2pi)/3 in ...

    Text Solution

    |

  20. How many solutions does the equation(8^x + 27^x)/(12^x +18^x) = 7/6hav...

    Text Solution

    |