Home
Class 12
MATHS
If a rg(z1)=170^0a n d arg(z2)70^0 , the...

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

Text Solution

Verified by Experts

`arg(z_(1)z_(2)) = arg(z_(1)) + arg(z_(2)) = 170^(@) + 70^(@) = 240^(@)`
Thus`z_(1),z_(2)` lies in the third quandrant . Hence, its principal argument is `-120^(@)`.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.2|9 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

If arg(z_(1))=170^(@) andarg (z_(2))=70^(@), then find the principal argument of z_(1)z_(2)

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) .

The principal argument of 2z^(2)+1-sqrt(3)i=0

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

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

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

If arg(z) lt 0, then find arg(-z) -arg(z) .

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

If arg (bar (z) _ (1)) = arg (z_ (2)) then

CENGAGE-COMPLEX NUMBERS-Examples
  1. If (sqrt(8)+i)^(50)=3^(49)(a+i b) , then find the value of a^2+b^2dot

    Text Solution

    |

  2. Show that (x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot

    Text Solution

    |

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

    Text Solution

    |

  4. Find the value of expression (cospi/2+is inpi/2)(cospi/(2^2)+is inpi/(...

    Text Solution

    |

  5. Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))...

    Text Solution

    |

  6. If z=((sqrt(3)+i)^(17))/((1-i)^(50)) , then find a m p(z)dot

    Text Solution

    |

  7. If z=x+i ya n dw=(1-i z)/(z-i) , show that |w|=1 z is purely real.

    Text Solution

    |

  8. It is given the complex numbers z(1) and z(2), |z(1)| =2 and |z(2)| ...

    Text Solution

    |

  9. Solve the equation z^(3) = barz (z ne 0)

    Text Solution

    |

  10. If 2z1//3z2 is a purely imaginary number, then find the value of "|"(z...

    Text Solution

    |

  11. Find the complex number satisfying the system of equations z^3+ omega^...

    Text Solution

    |

  12. Express the following in a + ib form: (i) ((cos theta+ isin theta...

    Text Solution

    |

  13. If z=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5 , then prove that Im(z)=0

    Text Solution

    |

  14. Prove that the roots of the equation x^4-2x^2+4=0 forms a rectangle.

    Text Solution

    |

  15. If z+1//z=2costheta, prove that |(z^(2n)-1)//(z^(2n)+1)|=|tanntheta|

    Text Solution

    |

  16. If z=x+iy is a complex number with x, y in Q and |z| = 1, then show ...

    Text Solution

    |

  17. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)++a(n...

    Text Solution

    |

  18. If |z1|=1,|z2|=2,|z3|=3,a n d|9z1z2+4z1z3+z2z3+3|=12 , then find the v...

    Text Solution

    |

  19. If alphaand betaare different complex numbers with |beta|=1,then fin...

    Text Solution

    |

  20. Prove that |z1+z2|^2=|z1|^2, ifz1//z2 is purely imaginary.

    Text Solution

    |