Home
Class 11
MATHS
z1a n dz2 are two distinct points in an ...

`z_1a n dz_2` are two distinct points in an Argand plane. If `a|z_1|=b|z_2|(w h e r ea ,b in R),` then the point `(a z_1//b z_2)+(b z_2//a z_1)` is a point on the line segment [-2, 2] of the real axis line segment [-2, 2] of the imaginary axis unit circle `|z|=1` the line with `a rgz=tan^(-1)2`

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

Z_1!=Z_2 are two points in an Argand plane. If a|Z_1|=b|Z_2|, then prove that (a Z_1-b Z_2)/(a Z_1+b Z_2) is purely imaginary.

Z_1!=Z_2 are two points in an Argand plane. If a|Z_1|=b|Z_2|, then prove that (a Z_1-b Z_2)/(a Z_1+b Z_2) is purely imaginary.

z_(1) , z_(2) are two distinct points in complex plane such that 2|z_(1)|=3|z_(2)| and z in C be any point z=(2z_(1))/(3z_(2))+(3z_(2))/(2z_(1)) such that

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| = |z-z_(2)|

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( z )_2dot

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)|= k|z-z_(2)|, k in R^(+), k ne 1

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| + |z-z_(2)| = |z_(1)-z_(2)|

If z_(1) and z_(2) are two fixed points in the Argand plane, then find the locus of a point z in each of the following |z-z_(1)| - |z-z_(2)|= |z_(1)-z_(2)|

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=- bar z _2dot

If A(z_(1)) and B(z_(2)) are two points in the Argand plane such that z_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0 , then triangleOAB , is

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the complex number z satisfying R e(z^2 =0),|z|=sqrt(3.)

    Text Solution

    |

  2. Given that the expression 2x^3+3p x^2-4x+p hs a remainder of 5 when di...

    Text Solution

    |

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

    Text Solution

    |

  4. Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i...

    Text Solution

    |

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

    Text Solution

    |

  6. 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

    |

  7. If (a" "+" "i b)" "(c" "+" "i d)" "(e" "+" "if)" "(g" "+" "i h)" "=" "...

    Text Solution

    |

  8. Analyze the roots of the equation (x-1)^3+(x-2)^3+(x-4)^3+(x-5)^3=0 by...

    Text Solution

    |

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

    Text Solution

    |

  10. If z=i^(i^(i)) where i=sqrt-1 then |z| is equal to

    Text Solution

    |

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

    Text Solution

    |

  12. If alpha and beta are different complex numbers with |beta|=1, then...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If z=x+i y and w=(1-i z)//(z-i) and |w| = 1 , then show that z is pure...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |