Home
Class 12
MATHS
If sqrt(5-12 i)+sqrt(5-12 i)=z , then pr...

If `sqrt(5-12 i)+sqrt(5-12 i)=z` , then principal value of `a rgz` can be `pi/4` b. `pi/4` c. `(3pi)/4` d. `-(3pi)/4`

A

`-(pi)/(4)`

B

`(pi)/(4)`

C

`(3pi)/(4)`

D

`-(3pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`sqrt(5-12i) = sqrt((3-2i)^(2)) = pm (3-2i)`
`sqrt(-5-12i)= sqrt((2-3i)^(2)) = pm (2-3i)`
`rArr z = sqrt(5-12i) + sqrt(5-12i) = sqrt((3-2i)^(2)) = pm (3-2i)`
`sqrt(-5-12i)= sqrt((2-3i)^(2)) = pm (2-3i)`
`rArr z = sqrt(5-12i) + sqrt(-5-12i)`
`=- 1-i, -5 + 5i,5-5i, 1+i`
Therefore, principal values of arg are `- 3pi//4, 3pi//4,-pi//4, pi//4`.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise (Comprehension)|34 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise MATRIX MATCH TYPE|9 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise (Single)|89 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

If sqrt(5-12i)+sqrt(-5-12i)=z ,then principal value of argz can be (pi)/(4) b.(pi)/(4) c.(3 pi)/(4) d.-(3 pi)/(4)

The principal value of the amplitude of (1+i) is pi b.(pi)/(12) c.(pi)/(4) d.(3 pi)/(4)

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=sqrt(3)-2+i, then principal value of argument z is (where i=sqrt(-1)-(5 pi)/(12)(2)(pi)/(12) (3) (7 pi)/(12) (4) (5 pi)/(12)

If a complex number z satisfies |2z+10+10i|<=5sqrt(3)-5, then the least principal argument of z is :(a)-(5 pi)/(6) (b) (11 pi)/(12)( c) -(3 pi)/(4)(d)-(2 pi)/(3)

Write the modulus and principal arguments of the complex no.z=4(cos((pi)/(4))+i sin((pi)/(4)))

If sin x+sqrt(3)cos x=sqrt(2) then general solution of x 2n pi+(pi)/(12) 2n pi-(pi)/(12) 2n pi+(5 pi)/(12) 2n pi-(5 pi)/(12)

The value of int_0^pi1/(5+3cosx)dx is pi//2 b. pi//4 c. 0 d. pi//8

The solution set of the equation 4s int h eta cos theta-2cos theta-2sqrt(3)s int_(h eta)+sqrt(3)=0 in the interval (0,2 pi) is {(3 pi)/(4),(7 pi)/(4)} (b) {(pi)/(3),(5 pi)/(3)}{(3 pi)/(4),pi,(pi)/(3)(5 pi)/(3)}(d){(pi)/(6),(5 pi)/(6),(11 pi)/(6)}

CENGAGE-COMPLEX NUMBERS-Exercise (Multiple)
  1. If z=omega,omega^2w h e r eomega is a non-real complex cube root of un...

    Text Solution

    |

  2. If a m p(z1z2)=0a n d|z1|=|z2|=1,t h e n z1+z2=0 b. z1z2=1 c. z1=z 2...

    Text Solution

    |

  3. If sqrt(5-12 i)+sqrt(5-12 i)=z , then principal value of a rgz can be ...

    Text Solution

    |

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

    Text Solution

    |

  5. If a^3+b^3+6a b c=8c^3&omega is a cube root of unity then: a , b , c a...

    Text Solution

    |

  6. Let z(1) and z(2) be two non -zero complex number such that |z(1)+z...

    Text Solution

    |

  7. If p =a + bomega + comega^(2),q = b + comega + aomega^(2), and r =c +...

    Text Solution

    |

  8. Let P(x) and Q(x) be two polynomials.Suppose that f(x) = P(x^3) + x Q(...

    Text Solution

    |

  9. If alpha is a complex constant such that a z^2+z+ alpha=0 has a ral ro...

    Text Solution

    |

  10. If z^3+3+2i(z+(-1+i a)=0 has on ereal roots, then the value of a lies ...

    Text Solution

    |

  11. Given that the complex numbers which satisfy the equation | z z ^3|+|...

    Text Solution

    |

  12. If the points A(z),B(-z),a n dC(1-z) are the vertices of an equilatera...

    Text Solution

    |

  13. If |z-3| = "min" {|z-1|,|z-5|}, then Re(z) equals to

    Text Solution

    |

  14. If z(1),z(2) are tow complex numberes (z(1) ne z(2)) satisfying |z(1)...

    Text Solution

    |

  15. If z1=a + ib and z2 = c + id are complex numbers such that |z1|=|z2|=...

    Text Solution

    |

  16. Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...

    Text Solution

    |

  17. If |z(1)| = sqrt(2), |z(2)| = sqrt(3) and |z(1) + z(2)| = sqrt((5-2sqr...

    Text Solution

    |

  18. Let four points z(1),z(2),z(3),z(4) be in complex plane such that |z...

    Text Solution

    |

  19. A rectangle of maximum area is inscribed in the circle |z-3-4i|=1. If ...

    Text Solution

    |

  20. If |z1|=15a d n|z2-3-4i|=5,t h e n (|z1-z2|)(m in)=5 b. (|z1-z2|)(m i...

    Text Solution

    |