Home
Class 12
MATHS
If arg(z) lt 0, then arg(-z)-arg(z)=...

If `arg(z) lt 0`, then `arg(-z)-arg(z)=`

A

`pi`

B

`-pi`

C

`pi/2`

D

`pi/2`

Text Solution

Verified by Experts

The correct Answer is:
A
Let arg(z) =-0 where `theta gt 0` ltgtgt It is evident from the figure that
`therefore "arg"(-z)-"arg"(z) = pi-theta-(-theta)=pi`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|15 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Exercise|131 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|59 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

Similar Questions

Explore conceptually related problems

If arg(z) lt 0, then find arg(-z) -arg(z) .

arg(bar(z))+arg(-z)={{:(pi",","if arg (z) "lt 0),(-pi",", "if arg (z) "gt 0):},"where" -pi lt arg(z) le pi . If arg(z) gt 0 , then arg (-z)-arg(z) is equal to

If z is purely imaginary and Im (z) lt 0 , then arg(i bar(z)) + arg(z) is equal to

arg(bar(z))=-arg(z)

arg(bar(z))+arg(-z)={{:(pi",","if arg (z) "lt 0),(-pi",", "if arg (z) "gt 0):},"where" -pi lt arg(z) le pi . If arga(4z_(1))-arg(5z_(2))=pi, " then " abs(z_(1)/z_(2)) is equal to

If arg (z)<0, then underset(pi)/(2)arg(-z)-arg(z) equals pi(b)-pi(d)-(pi)/(2)(d)(pi)/(2)

OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Section I - Solved Mcqs
  1. If (1+i)z=(1-i)barz, then z is equal to

    Text Solution

    |

  2. Let z=(costheta+isintheta)/(costheta-isintheta), pi/4 lt theta lt pi/...

    Text Solution

    |

  3. If arg(z) lt 0, then arg(-z)-arg(z)=

    Text Solution

    |

  4. The value of {sin(logi^i)}^3+{cos(logi^i)}^3, is

    Text Solution

    |

  5. If z=a+ib satisfies "arg"(-1)="arg"(z+3i), then (a-1):b=

    Text Solution

    |

  6. If the area of the triangle on the complex plane formed by the points ...

    Text Solution

    |

  7. If the area of the triangle on the complex plane formed by complex num...

    Text Solution

    |

  8. If x^2+x+1=0 then the value of (x+1/x)^2+(x^2+1/(x^2))^2+...+(x^27+1/(...

    Text Solution

    |

  9. If x^2-x+1=0 then the value of sum[n=1]^[5][x^n+1/x^n]^2 is:

    Text Solution

    |

  10. The value of alpha^(-n)+alpha^(-2n), n in N and alpha is a non-real cu...

    Text Solution

    |

  11. If alpha is a non-real fourth root of unity, then the value of alpha^(...

    Text Solution

    |

  12. If 1,alpha,alpha^(2),……….,alpha^(n-1) are n^(th) root of unity, the va...

    Text Solution

    |

  13. If omega is an imaginary cube root of unity, then find the value of (1...

    Text Solution

    |

  14. If alpha is a non-real fifth root of unity, then the value of 3^(|1+a...

    Text Solution

    |

  15. If Zr=cos((2rpi)/5)+isin((2rpi)/5),r=0,1,2,3,4,... then z1z2z3z4z5 is...

    Text Solution

    |

  16. z is a complex number satisfying z^(4)+z^(3)+2z^(2)+z+1=0, then |z| is...

    Text Solution

    |

  17. if (5z2)/(7z1) is purely imaginary number then |(2z1+3z2)/(2z1-3z2) |...

    Text Solution

    |

  18. The locus of point z satisfying R e(1/z)=k ,w h e r ek is a nonzero re...

    Text Solution

    |

  19. If z lies on the circle I z l = 1, then 2/z lies on

    Text Solution

    |

  20. The maximum value of |z| where z satisfies the condition |z+(2/z)|=2 i...

    Text Solution

    |