Home
Class 12
MATHS
Solve the equation z^(3) = barz (z ne 0)...

Solve the equation `z^(3) = barz (z ne 0)`

Text Solution

Verified by Experts

As `zne0,`
`|z^(3)|=|bar(z)|`
`implies" "|z|^(3)=|bar(z)|`
`implies" "|z|^(3)=|z|`
`implies" "|z|=1`
`:." "z^(3)=bar(z)`
`implies" "z^(4)=zbar(z)=|z|^(2)=1`
`implies" "z=+-1,+-i`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise SLOVED EXAMPLES|15 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise EXERCISE3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

The equation z^3=barz has

Solve the equation z^3= z (z!=0)dot

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

Solve the equation |z|=z+1+2idot

Solve the equation for x, y, z and t, if 2[(x, y),(z,t)]+3[(1,-1),(0,2)]=3[(3,5),(4,6)]

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

The roots of the cubic equation (z+ ab)^(3) = a^(3) , such that a ne 0 , respresent the vertices of a trinagle of sides of length

If z_1,z_2,z_3 are any three roots of the equation z^6=(z+1)^6, then arg((z_1-z_3)/(z_2-z_3)) can be equal to

Solve the system of equations in x,y and z satisfying the following equations x+[y]+{z}=3.1, y+[z]+{x}=4.3 and z+[x]+{y}=5.4

Prove that the equations kx + y + z = 1, x + ky + z = k and x + y + kz = k^(2) will have unique solution when k ne 1 and k ne -2 . Solve the equations in this case.

CENGAGE PUBLICATION-COMPLEX NUMBERS-ILLUSTRATION
  1. If z=x+i y and w=(1-i z)/(z-i) , show that |w|=1 z is purely real.

    Text Solution

    |

  2. It is given the complex numbers z(1) and z(2), |z(1)| =2 and |z(2)| ...

    Text Solution

    |

  3. Solve the equation z^(3) = barz (z ne 0)

    Text Solution

    |

  4. If 2z1//3z2 is a purely imaginary number, then find the value of "|"(z...

    Text Solution

    |

  5. Find the complex number satisfying the system of equations z^3+ omega^...

    Text Solution

    |

  6. Express the following in a + ib form: (i) ((cos theta+ isin theta...

    Text Solution

    |

  7. Let z = ((sqrt(3))/(2) + (i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5). If ...

    Text Solution

    |

  8. Prove that the roots of the equation x^4-2x^2+4=0 forms a rectangle.

    Text Solution

    |

  9. If z + 1/z = 2costheta, prove that |(z^(2n)-1)//(z^(2n)+1)|=|tannthet...

    Text Solution

    |

  10. If z=x+i y is a complex number with x ,y in Qa n d|z|=1, then show th...

    Text Solution

    |

  11. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)+.......

    Text Solution

    |

  12. If |z1|=1,|z2|=2,|z3|=3,a n d|9z1z2+4z1z3+z2z3|=12 , then find the val...

    Text Solution

    |

  13. If alpha\ a n d\ beta are different complex numbers with |beta|=1,\ fi...

    Text Solution

    |

  14. Given that |z1+z2|^2=|z1|^2+|z2|^2, prove that z1/z2 is purely imagina...

    Text Solution

    |

  15. Let |(z(1) - 2z(2))//(2-z(1)z(2))|= 1 and |z(2)| ne 1, where z(1) and...

    Text Solution

    |

  16. If z1a n dz2 are two complex numbers and c >0 , then prove that |z1+z2...

    Text Solution

    |

  17. If z1, z2, z3, z4 are the affixes of four point in the Argand plane, z...

    Text Solution

    |

  18. if |z1+z2|=|z1|+|z2|, then prove that a r g(z1)=a r g(z2) if |z1-z2|=...

    Text Solution

    |

  19. Show that the area of the triangle on the Argand diagram formed by the...

    Text Solution

    |

  20. Find the minimum value of |z-1| if ||z-3|-|z+1||=2.

    Text Solution

    |