Home
Class 11
MATHS
If a rg(z1)=170^0 and arg(z2)=70^0 , th...

If `a rg(z_1)=170^0 and arg(z_2)=70^0` , then find the principal argument of `z_1z_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

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

If arg (z_(1))=(17pi)/18 and arg (z_(2))=(7pi)/18, find the principal argument of z_(1)z_(2) and (z_(1)//z_(2)).

If arg(z_(1))=(2pi)/3 and arg(z_(2))=pi/2 , then find the principal value of arg(z_(1)z_(2)) and also find the quardrant of z_(1)z_(2) .

If z_(1) and z_(2) are conjugate to each other , find the principal argument of (-z_(1)z_(2)) .

If arg (z_(1)z_(2))=0 and |z_(1)|=|z_(2)|=1 , then

If arg(z-1)=arg(z+2i) , then find (x-1):y , where z=x+iy

For z= sqrt3-i , find the principal, value arg(z)

Let z_1, z_2,z_3 be complex numbers (not all real) such that |z_1|=|z_2|=|z_3|=1 and 2(z_1+z_2+z_3)-3z_1 z_2 z_3 is real. Then, Max (arg(z_1), arg(z_2), arg(z_3)) (Given that argument of z_1, z_2, z_3 is possitive ) has minimum value as (kpi)/6 where (k+2) is

If arg(z-1)=arg(z+3i) , then find (x-1):y , where z=x+iy .

If |z_(1)|=|z_(2)| and arg (z_(1))+"arg"(z_(2))=0 , then

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

    Text Solution

    |

  2. If z1=9y^2-4-10ix, z2=8y^2-20i, where z1=overline z2, then find z=x+i...

    Text Solution

    |

  3. If a rg(z1)=170^0 and arg(z2)=70^0 , then find the principal argument...

    Text Solution

    |

  4. z1, z2 and z3 are the vertices of an isosceles triangle in anticlockwi...

    Text Solution

    |

  5. function f , R ->R , f(x) = (3x^2+mx+n)/(x^2+1) , if the range of func...

    Text Solution

    |

  6. If z(1) and z(2) are conjugate to each other , find the principal argu...

    Text Solution

    |

  7. If a is a complex number such that |a|=1, then find the value of a, s...

    Text Solution

    |

  8. If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=...

    Text Solution

    |

  9. Find the value of expression (cospi/2+i sin(pi/2))(cos(pi/(2^2))+i si...

    Text Solution

    |

  10. Solve for z , i.e. find all complex numbers z which satisfy |z|^2-2i z...

    Text Solution

    |

  11. If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' a...

    Text Solution

    |

  12. If a ,b are complex numbers and one of the roots of the equation x^2+a...

    Text Solution

    |

  13. If |z1|=|z2|=1, then prove that |z1+z2|= |1/z1+1/z2∣

    Text Solution

    |

  14. If (a x^2+c)y+(a^(prime)x^2+c^(prime) )=0 and x is a rational function...

    Text Solution

    |

  15. Find the principal argument of the complex number sin(6pi)/5+i(1+cos(6...

    Text Solution

    |

  16. For x in (0,1) , prove that i^(2i+3) ln((i^3x^2+2x+i)/(i x^2+2x+i^3))=...

    Text Solution

    |

  17. The sum of the non-real root of (x^2+x-2)(x^2+x-3)=12 is -1 b. 1 c. -...

    Text Solution

    |

  18. If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1....

    Text Solution

    |

  19. The number of roots of the equation sqrt(x-2)(x^2-4x+3)=0 is (A) Thre...

    Text Solution

    |

  20. If z1, z2a n dz3, z4 are two pairs of conjugate complex numbers, then ...

    Text Solution

    |