Home
Class 11
MATHS
Find all non zero complex numbers z sati...

Find all non zero complex numbers z satisfying `barz=iz^2`

Text Solution

Verified by Experts

The correct Answer is:
`z=0,i, (sqrt3)/(2)-(1)/(2)i,-(sqrt3)/(2)-(1)/(2)i`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise Very Short Answer Type Questions(True or False|5 Videos

  • BINOMIAL THEOREM

    CBSE COMPLEMENTARY MATERIAL|Exercise LONG ANSWER TYPE QUESTIONS(Section-D)|16 Videos

  • COORDINATE GEOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise section(D) (Long Answer Type Questions ) (6 Marks)|21 Videos

Similar Questions

Explore conceptually related problems

Find the non-zero complex numbers z satisfying z=iz^(2)

Find all complex numbers satisfying barz = z^2 .

Find all complex number z satisfying bar(z)+1=iz^(2)+|z|^(2)

Find number of all complex numbers z satisfying bar(z) =iz^2

The nonzero complex number Z satisfying Z=iZ^(2) is

Modulus of nonzero complex number z satifying barz + z =0 and |z|^(2)-4iz=z^(2) is _____.

Let z_(1),z_(2) and z_(3) be non-zero complex numbers satisfying z^(2)=bar(iz), where i=sqrt(-1). What is z_(1)+z_(2)+z_(3) equal to ?

CBSE COMPLEMENTARY MATERIAL-COMPLEX NUMBERS AND QUADRATIC EQUATIONS -Short Answer Type Questions
  1. Prove that: x^4=4=(x+1+i)(x+1-i)(x-1+i(x-1-i)dot)

    Text Solution

    |

  2. Show that |(z -2)/(z - 3)| = 2 represents a circle, find its centre ...

    Text Solution

    |

  3. Find all non zero complex numbers z satisfying barz=iz^2

    Text Solution

    |

  4. If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2...

    Text Solution

    |

  5. If z1,z2 are complex numbers such that, (2z1)/(3z2) is purely imaginar...

    Text Solution

    |

  6. If z1 and z2 are complex numbers such that, |1-bar z1z2|^(2)-|z1-z(2^(...

    Text Solution

    |

  7. Find the number of solutions of z^2+|z|^2=0.

    Text Solution

    |

  8. If z1,z2 are complex numbers such that, |(z1-3z2)/(3-z1.bar z2)|=1 and...

    Text Solution

    |

  9. Evaluate x^(4) -4x^(3)+4x^(2)+8x+44, when x=3+2i

    Text Solution

    |

  10. Complex number z1 and z2 satisfy z+barz=2|z-1| and arg (z1-z2) = pi/4 ...

    Text Solution

    |

  11. Solve the following quadratic equation: \ 2x^2-(3+7i)x+(9i-3)=0

    Text Solution

    |

  12. What is the locus of z , if amplitude of (z-2-3i) is pi/2?

    Text Solution

    |

  13. If z=x+i ya n dw=(1-i z)/(z-i) , show that |w|=1 z is purely real.

    Text Solution

    |

  14. Express the following complex numbers in the form r(costheta+isintheta...

    Text Solution

    |

  15. Express the complex number in the form r(cos theta+isin theta) (ii)1-s...

    Text Solution

    |

  16. If (1+i)/(1+2^2i)xx(1+3^2i)/(1+4^2i)xx.......xx(1+(2n-1)^2i)/(1+(2n)^2...

    Text Solution

    |

  17. Find real values of xa n dy for which the complex numbers -3+i x^2ya n...

    Text Solution

    |

  18. The complex numbers z1 z2 and z3 satisfying (z1-z3)/(z2-z3) =(1- i sqr...

    Text Solution

    |

  19. If f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is (|z|)/2 (b) |z| ...

    Text Solution

    |

  20. If z1,z2 and z3 are complex numbers such that |z1|=|z2|=|z3|= |1/z1+1/...

    Text Solution

    |