Home
Class 11
MATHS
Consider two complex numbers alpha and b...

Consider two complex numbers `alpha` and `beta` as `alpha=[(a+b i)//(a-b i)]^2+[(a-b i)//(a+b i)]^2`, where a ,b in R and `beta=(z-1)//(z+1), w here |z|=1,` then find the correct statement:

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 w=z/[z-1/(3i)] and |w|=1, then find the locus of z

Find the modulus of the complex number z=1+i

Find the amplitude of the complex number z=1+i .

Let z_1 and z_2 , be two complex numbers with alpha and beta as their principal arguments such that alpha+beta gt pi then principal arg(z_1z_2) is given by:

If z=-i-1 is a complex number,then arg (z) will be

Find the sum and product of the two complex numbers z_1=2+3i and z=-1+5i .

For any two complex numbers z1,z2 and any real numbers a a n d b , | a z 1 - b z 2 | 2 + | b z 1 + a z 2 | 2 = aa n db ,|a z_1-b z_2|^2+|b z_1+a z_2|^2=

The complex number z satisfying the equation |z-i|=|z+1|=1 is

If tan (alpha + beta) = a + b " and " tan ( alpha -beta) = a-b, "then show that, " a tan alpha - b tan beta = a^(2)-b^(2)

If t and c are two complex numbers such that |t|!=|c|,|t|=1a n dz=(a t+b)/(t-c), z=x+i ydot Locus of z is (where a, b are complex numbers) a. line segment b. straight line c. circle d. none of these

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Given that the expression 2x^3+3p x^2-4x+p has a remainder of 5 when d...

    Text Solution

    |

  2. z1a n dz2 are two distinct points in an Argand plane. If a|z1|=b|z2|(w...

    Text Solution

    |

  3. Consider two complex numbers alpha and beta as alpha=[(a+b i)//(a-b i)...

    Text Solution

    |

  4. In how many points the graph of f(x)=x^3+2x^2+3x+4 meets the x-axis ...

    Text Solution

    |

  5. If x^2+x+1=0 then the value of (x+1/x)^2+(x^2+1/(x^2))^2+...+(x^27+1/(...

    Text Solution

    |

  6. If (a+ib)(c+id)(e+if)(g+ih)=A+iB, then show that (a^2+b^2)(c^2+d^2)(e^...

    Text Solution

    |

  7. Find the roots of the equation x+1/x=3

    Text Solution

    |

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

    Text Solution

    |

  9. If z=i^(i^(i)) where i=sqrt-1 then find the value of |z|

    Text Solution

    |

  10. Find the values of a for which the roots of the equation x^2+a^2=8x+6...

    Text Solution

    |

  11. If alpha and beta are different complex numbers with absbeta=1. then f...

    Text Solution

    |

  12. If z=i log(2-sqrt3), then cosz= a. -1 b. (-1)/2 c. ...

    Text Solution

    |

  13. If f(x)=x^3-x^2+a x+b is divisible by x^2-x , then find the value of...

    Text Solution

    |

  14. z=x+iy and w=(1-iz)/(1+iz) and |w|=1 ,prove that z is purely real

    Text Solution

    |

  15. If the equation z^4+a1z^3+a2z^2+a3z+a4=0 where a1,a2,a3,a4 are real co...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |