Home
Class 11
MATHS
If |z1/z2|=1 and arg (z1z2)=0 , then ...

If `|z_1/z_2|=1` and `arg (z_1z_2)=0` , then a. `z_1 = z_2` b. `|z_2|^2 = z_1*z_2` `c. z_1*z_2 = 1` d. none of these

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If |z|=1 and z'=(1+z^(2))/(z) , then

If absz_1=absz_2=absz_3=1 and z_1+z_2+z_3=0 , then z_1, z_2, z_3 are vertices of

If z_1nez_2 and abs(z_2)=1 the abs((z_1-z_2)/(1-barz_1z_2)) =

If a rg(z_1)=170^0 and arg(z_2)=70^0 , then find the principal argument of z_1z_2dot

If |z_1-z_0|=|z_2-z_0|=a and amp((z_2-z_0)/(z_0-z_1))=pi/2 , then find z_0

For two unimodular complex number z_1a n dz_2 [[barz_1, -z_2], [barz_2, z_1]]^(-1) [[(z_1, z_2], [-barz_2, barz_1]]^(-1) is equal to [(z_1, z_2), (z_1bar, z_2bar)]^ b. [1 0 0 1] c. [1//2 0 0 1//2] d. none of these

If |z_1|=|z_2|=|z_3|=1 then value of |z_1-z_3|^2+|z_3-z_1|^2+|z_1-z_2|^2 cannot exceed

If z_1a n dz_2 are complex numbers and u=sqrt(z_1z_2) , then prove that |z_1|+|z_2|=|(z_1+z_2)/2+u|+|(z_1+z_2)/2-u|

If z_1, z_2 are two complex numbers (z_1!=z_2) satisfying |z_1^2-z_2^2|=| z_ 1^2+ z _2 ^2-2( z _1)( z _2)| , then a. (z_1)/(z_2) is purely imaginary b. (z_1)/(z_2) is purely real c. |a r g z_1-a rgz_2|=pi d. |a r g z_1-a rgz_2|=pi/2

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let f(x)=a x^2+b x+c be a quadratic expression having its vertex at (3...

    Text Solution

    |

  2. If |z|=2a n d(z1-z3)/(z2-z3)=(z-2)/(z+2) , then prove that z1, z2, z3...

    Text Solution

    |

  3. If |z1/z2|=1 and arg (z1z2)=0 , then a. z1 = z2 b. |z2|^2 = z1*z2 ...

    Text Solution

    |

  4. Find the least value of n such that (n-2)x^2+8x+n+4>0,AAx in R ,w h ...

    Text Solution

    |

  5. The common roots of the equations z^3+2z^2+2z+1=0 and z^1985+z^100+1=0...

    Text Solution

    |

  6. If z1 + z2 + z3 + z4 = 0 where bi in R such that the sum of no two ...

    Text Solution

    |

  7. If the inequality (m x^2+3x+4)//(x^2+2x+2)<5 is satisfied for all x i...

    Text Solution

    |

  8. If |(z-2)//(z-3)|=2 represents a circle, then find its radius.

    Text Solution

    |

  9. If z1 is a root of the equation a0z^n+a1z^(n-1)+........+ (a(n-1)) z ...

    Text Solution

    |

  10. If f(x)=(a1x+b1)^2+(a2x+b2)^2+...+(an x+bn)^2 , then prove that (a1b1+...

    Text Solution

    |

  11. If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of...

    Text Solution

    |

  12. If |2z-1|=|z-2|a n dz1, z2, z3 are complex numbers such that |z1-alph...

    Text Solution

    |

  13. If (cgt 0) and 2ax^2+3bx+5c=0 does not have any real roots, then prove...

    Text Solution

    |

  14. Find the number of complex numbers which satisfies both the equations ...

    Text Solution

    |

  15. Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number...

    Text Solution

    |

  16. If a x^2+b x+6=0 does not have distinct real roots, then find the leas...

    Text Solution

    |

  17. |z-2-3i|^2+|z-4-3i|^2=lambda represents the equation of the circle wit...

    Text Solution

    |

  18. Match the statements/expressions given in column I with the values g...

    Text Solution

    |

  19. A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)...

    Text Solution

    |

  20. If (sqrt(8)+i)^(50)=3^(49)(a+i b) , then find the value of a^2+b^2dot

    Text Solution

    |