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 PUBLICATION|Exercise SLOVED EXAMPLES|15 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise EXERCISE3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

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

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

If z^2+abs(z)^2=0 then find the imaginary value of z

if arg(z+a)=pi/6 and arg(z-a)=(2pi)/3 then

If z is a complex number, then find the minimum value of |z|+|z-1|+|2z-3|dot

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

If z_(1)=3i and z_(2)=-1-i , where i=sqrt(-1) find the value of arg ((z_(1))/(z_(2)))

If |z_1|=1,|z_2|=2,|z_3|=3,a n d|9z_1z_2+4z_1z_3+z_2z_3|=12 , then find the value of |z_1+z_2+z_3|dot

If |z_1-1|lt=1,|z_2-2|lt=2,|z_(3)-3|lt=3, then find the greatest value of |z_1+z_2+z_3|dot

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:

CENGAGE PUBLICATION-COMPLEX NUMBERS-ILLUSTRATION
  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 (cos(pi/2)+isin(pi/2))(cos(pi/(2^2))+isin...

    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 y and w=(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. Let z = ((sqrt(3))/(2) + (i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5). If ...

    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)|=|tannthet...

    Text Solution

    |

  16. If z=x+i y is a complex number with x ,y in Qa n d|z|=1, then show th...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. If alpha\ a n d\ beta are different complex numbers with |beta|=1,\ fi...

    Text Solution

    |

  20. Given that |z1+z2|^2=|z1|^2+|z2|^2, prove that z1/z2 is purely imagina...

    Text Solution

    |