Home
Class 11
MATHS
If z1a n dz2 are two complex numbers and...

If `z_1a n dz_2` are two complex numbers and `c >0` , then prove that `|z_1+z_2|^2lt=(1+c)|z_1|^2+(1+c^(-1))|z_2|^2dot`

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 two complex number z_1a n d\ z_2 prove that: |z_1-z_2|lt=|z_1|+|z_2|

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|

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2 +|\z_1-z_2|^2=2[|\z_1|^2+|\z_2|^2]

For any two complex number z_1a n d\ z_2 prove that: |z_1+z_2|geq|z_1|-|z_2|

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|geq|z_1|-|z_2|

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2=|\z_1|^2+|\z_2|^2+2Re bar z_1 z_2

If z_1 and z_2 are two complex numbers such that |z_1|lt1lt|z_2| then prove that |(1-z_1barz_2)/(z_1-z_2)|lt1

if omega is the nth root of unity and Z_1 , Z_2 are any two complex numbers , then prove that . Sigma_(k=0)^(n-1)| z_1+ omega^k z_2|^2=n{|z_1|^2+|z_2|^2} where n in N

If z_(1), z_(2) in C (set of complex numbers), prove that |z_(1) + z_(2)| le |z_(1)| + |z_(2)|

For any two complex numbers z_1 and z_2 , prove that Re(z_1z_2)=Re(z_1) Re(z_2)-Im(z_1) Im(z_2) .

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the equation z^4+a1z^3+a2z^2+a3z+a4=0 where a1,a2,a3,a4 are real co...

    Text Solution

    |

  2. If f(x)=x^3-3x^2+2x+a is divisible by x-1, then find the remainder whe...

    Text Solution

    |

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

    Text Solution

    |

  4. Suppose A is a complex number and n in N , such that A^n=(A+1)^n=1, t...

    Text Solution

    |

  5. Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^...

    Text Solution

    |

  6. If z1, z2, z3 be the affixes of the vertices A, B and C of a triangle...

    Text Solution

    |

  7. The number of complex numbers z such that |z|=1 and |z/ barz + barz/z...

    Text Solution

    |

  8. Given that x^2-3x+1=0, then the value of the expression y=x^9+x^7+x^(-...

    Text Solution

    |

  9. If i z^4+1=0, then prove that z can take the value cospi//8+isinpi//...

    Text Solution

    |

  10. Find the value of x such that ((x+alpha)^n-(x+beta)^n)/(alpha-beta)=(s...

    Text Solution

    |

  11. Suppose a ,b ,c in I such that the greatest common divisor for x^2+a ...

    Text Solution

    |

  12. Find the value of following expression: [(1-cospi/(10)+isinpi/(10))/(1...

    Text Solution

    |

  13. Dividing f(z) by z- i, we obtain the remainder i and dividing it by z...

    Text Solution

    |

  14. If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consec...

    Text Solution

    |

  15. If z1, z2 in C ,z1^2+z2^2 in R ,z1(z1^2-3z2^2)=2 and z2(3z1^2-z2^2)...

    Text Solution

    |

  16. If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamm...

    Text Solution

    |

  17. If x+y+z=12 andx^2+y^2+z^2=96 and 1/x+1/y+1/z=36 , then the value x^3+...

    Text Solution

    |

  18. Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4), where n is a pos...

    Text Solution

    |

  19. The set {R e((2i z)/(1-z^2)): zi sacom p l e xnu m b e r ,|z|=1,z=+-1}...

    Text Solution

    |

  20. If the equation x^2+ax+bc=0" and " x^2-bx+ca=0 have a common root, the...

    Text Solution

    |