Home
Class 11
MATHS
If z!=0 is a complex number, then prove ...

If `z!=0` is a complex number, then prove that `R e(z)=0 rArr Im(z^2)=0.`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

State true or false for the following. If z is a complex number such that z ne 0 " and Re " (z)= 0 " then Im" (z^(2)) = 0 .

If z!=0 be a complex number and a rg(z)=pi/4, then R e(z)=I m(z)on l y R e(z)=I m(z)>0 R e(z^2)=I m(z^2) (d) None of these

Find the complex number z such that z^2+|z|=0

If z is a complex number such that |z-1|= |z+1| , show that Re(z)= 0

If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+(z^2+1/z^2)^2+....+(z^6+1/z^6)^2 is

If z_1,z_2 are two complex numbers such that Im(z_1+z_2)=0,Im(z_1z_2)=0 , then:

z is a complex number such that |Re(z)| + |Im (z)| = 4 then |z| can't be

z is a complex number such that |Re(z)| + |Im (z)| = 4 then |z| can't be

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the square roots of the following: (i) 7-24 i

    Text Solution

    |

  2. True or false The equation2x^2+3x+1=0 has an irrational root.

    Text Solution

    |

  3. If z!=0 is a complex number, then prove that R e(z)=0 rArr Im(z^2)=0.

    Text Solution

    |

  4. If l ,m ,n are real and l!=m , then the roots of the equation (l-m)x...

    Text Solution

    |

  5. Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0\ ,...

    Text Solution

    |

  6. If x ,y and z are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2x ...

    Text Solution

    |

  7. If (x+i y)^3=u+i v , then show that u/x+v/y=4(x^2-y^2)

    Text Solution

    |

  8. Let a >0,b >0 and c >0 . Then, both the roots of the equation a x^2+b ...

    Text Solution

    |

  9. If the sum of square of roots of the equation x^2+(p+i q)x+3i=0 is 8, ...

    Text Solution

    |

  10. Column I, Column II y=(x^2-2x+4)/(x^2+2x+4),x in R ,t h e ny c a n...

    Text Solution

    |

  11. If sqrt(x+i y)=+-(a+i b), then findsqrt( x-i ydot)

    Text Solution

    |

  12. Match the following for the equation x^2+a|x1=0,w h e r ea is a parame...

    Text Solution

    |

  13. Find the ordered pair (x ,y) for which x^2-y^2-i(2x+y)=2idot

    Text Solution

    |

  14. If a ,b ,c are non zero complex numbers of equal modlus and satisfy a ...

    Text Solution

    |

  15. Column I, Column II If a ,b ,c ,a n dd are four zero real number...

    Text Solution

    |

  16. Let z be not a real number such that (1+z+z^2)//(1-z+z^2) in R , then...

    Text Solution

    |

  17. Let a is a real number satisfying a^3+1/(a^3)=18 . Then the value of a...

    Text Solution

    |

  18. Find non zero integral solutions of |1-i|^x=2^xdot

    Text Solution

    |

  19. If (1+i)(1+2i)(1+3i)......(1+n i)=(x+i y) , show that 2. 5. 10...... (...

    Text Solution

    |

  20. If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c<0 , then wh...

    Text Solution

    |