Home
Class 12
MATHS
If z=((1+isqrt(3))/(1+i))^(25), then ar...

If `z=((1+isqrt(3))/(1+i))^(25)`, then arg(z) is equal to

A

`(pi)/(12)`

B

`-(pi)/(12)`

C

`(7pi)/(12)`

D

`(3pi)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
1
`z=(1+isqrt3)^(25)/(1+i)^(25)=(2^(25).(e^(ipi//3))^(25))/(2^(25/2).(e^(ipi//4))^(25))`
`=2^(25/2)e^(i((25pi)/(12)))=e^(25/(2))e^(i((pi)/(12)))`
or `(2pi+(pi)/(12))=(25pi)/(12)`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 1

    CAREER POINT|Exercise PART (C) - MATHS|30 Videos

  • MOCK TEST 2

    CAREER POINT|Exercise PART ( C)- MATHS|30 Videos

Similar Questions

Explore conceptually related problems

If z=((1+i sqrt(3))/(1+i))^(25), then arg(z) is equal to

If z=(1+2i)/(1-(1-i)^(2)), then arg (z) equals a.0 b.(pi)/(2) c.pi d .non of these

If z=(-2)/(1+isqrt(3)) , then the value of "arg"(z) is a. pi b. pi/4 c. pi/3 d. (2pi)/3

If z=1+i sqrt(3), then |arg(z)|+|arg(bar(z))| equals to

" If "z=sqrt((1-i)/(1+i))" ,then arg z"=

|z_(1)|=|z_(2)| and arg((z_(1))/(z_(2)))=pi, then z_(1)+z_(2) is equal to

CAREER POINT-MOCK TEST 10-PART (C) - MATHS
  1. The interval in which the function f(x)=sin x-cos x -ax +b decreases f...

    Text Solution

    |

  2. Set of values of b for which local extrema of the function f(x) are po...

    Text Solution

    |

  3. If z=((1+isqrt(3))/(1+i))^(25), then arg(z) is equal to

    Text Solution

    |

  4. In which of the following is false

    Text Solution

    |

  5. The number of real roots of (x-1)^(4)+(x+1)^(4)=16 is

    Text Solution

    |

  6. The differential equation (dy)/(dx)+P y=Q y^n ,\ n >2 can be reduced t...

    Text Solution

    |

  7. Two tangents are drawn to the hyperbola x^2/a^2-y^2/b^2=1 such that pr...

    Text Solution

    |

  8. The value of int2^("mx").3^("nx")dx (when m, n in N) is equal to:

    Text Solution

    |

  9. dx is equal to ([.] is g.i.f.)

    Text Solution

    |

  10. if y=tan^(-1)x+"tan"^(-1)(1)/(x)+sec^(-1)x,then" "yin

    Text Solution

    |

  11. A student is to answer 10 out of 13 questions in an examination such t...

    Text Solution

    |

  12. One of the roots of the equation 8x^(3)-6x+1=0 is

    Text Solution

    |

  13. In the interval [-pi/2,pi/2] the equation log(sin theta)(cos 2 theta)=...

    Text Solution

    |

  14. Let f(x)=(x^(2)-3x+2)(x^(3)-6x^(2)+11x-6)|+|sin(x+(pi)/(4))| The set...

    Text Solution

    |

  15. Let p : price increases q : Demand falls The symbolic statements fo 'i...

    Text Solution

    |

  16. Angle of elevation of top of a tower from a point 'A' due E30^(@)N of ...

    Text Solution

    |

  17. In an experiment with 15 observations of x the following results were ...

    Text Solution

    |

  18. The shortest distance between line (x-3)/(3)=(y-8)/(-1)=(z-3)/(1) and ...

    Text Solution

    |

  19. Ratio of volumes of tetrahedrons having coterminus edees bara+barb,bar...

    Text Solution

    |

  20. Table IfDelta(r)=|{:(,(2r), x, N(N+1)),(,(6r^(2)-1),y, N^(2)(2N+3)),...

    Text Solution

    |