Home
Class 12
MATHS
Number of solutions of the equation z^3+...

Number of solutions of the equation `z^3+[3(barz)^2]/|z|=0` where z is a complex number is

A

2

B

3

C

6

D

5

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `z^(3)+(3(barz)^(2))/(|z|)=0`
Let `z=re^(itheta)`
`rArr r^(3)e^(i3theta)+3re^(-2theta)=0`
Since r cannot be zero, so
`re^(i5theta)=-3`
Which will hold for r = 3 and five values of `theta`. Thus, there are five solution.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise (Multiple)|49 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise (Comprehension)|34 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.11|6 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

The number of solutions of the equation z^(3)+(3(barz)^(2))/(|z|)=0 (where, z is a complex number) are

Number of solutions of the equation z^(3)+(3(bar(z))^(2))/(|z|)=0 where z is a complex number is

What is the number of distinct solutions of the equation z^(2)+|z|=0 (where z is a complex number)? (a) One (b) Two (c) Three (d) Five

The number of solutions of the equation z^(2)+z=0 where z is a a complex number,is

Number of solutions of the equation z^(2)+|z|^(2)=0 , where z in C , is

Solve the equation z^(2)+|z|=0, where z is a complex number.

Solve the equation, z^(2) = bar(z) , where z is a complex number.

CENGAGE-COMPLEX NUMBERS-Exercise (Single)
  1. if |z^2-1|=|z|^2+1 then z lies on

    Text Solution

    |

  2. If z=x+iy (x, y in R, x !=-1/2), the number of values of z satisfying ...

    Text Solution

    |

  3. Number of solutions of the equation z^3+[3(barz)^2]/|z|=0 where z is a...

    Text Solution

    |

  4. Number of ordered pairs(s) (a, b) of real numbers such that (a+ib)^200...

    Text Solution

    |

  5. The equation az^(3) + bz^(2) + barbz + bara = 0 has a root alpha, wh...

    Text Solution

    |

  6. If k>0, |z|=\w\=k, and alpha=(z-bar w)/(k^2+zbar(w)), then Re(alpha) ...

    Text Solution

    |

  7. z1a n dz2 are two distinct points in an Argand plane. If a|z1|=b|z2|(w...

    Text Solution

    |

  8. If z is a comple number such that -(pi)/(2) lt "arg z" le (pi)/(2), ...

    Text Solution

    |

  9. If cos alpha + 2 cos beta +3 cos gamma = sin alpha + 2 sin beta + 3 s...

    Text Solution

    |

  10. If alpha,beta be the roots of the equation u^2-2u+2=0 and if cottheta...

    Text Solution

    |

  11. If z=(i)^{(i)^(i)} w h e r e i=sqrt(-1),t h e n|z| is equal to

    Text Solution

    |

  12. lf z = ilog(2-sqrt(-3)), then cos z =

    Text Solution

    |

  13. If |z|=1, then the point representing the complex number -1+3z will li...

    Text Solution

    |

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

    Text Solution

    |

  15. If z is complex number, then the locus of z satisfying the condition |...

    Text Solution

    |

  16. The greatest positive argument of complex number satisfying |z-4|=R e(...

    Text Solution

    |

  17. If ta n dc are two complex numbers such that |t|!=|c|,|t|=1a n dz=(a t...

    Text Solution

    |

  18. If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight ...

    Text Solution

    |

  19. Let C1 and C2 are concentric circles of radius 1and 8/3 respectively ...

    Text Solution

    |

  20. If |z-2-i|=|z|sin(pi/4-a r g z)| , where i=sqrt(-1) ,then locus of z,...

    Text Solution

    |