Home
Class 12
MATHS
If z(1)andz(2) be two non-zero complex n...

If `z_(1)andz_(2)` be two non-zero complex numbers such that `|z_(1)+z_(2)|=|z_(1)|+|z_(2)|`, then prove that `argz_(1)-argz_(2)=0`.

Text Solution

Verified by Experts

The correct Answer is:
`=>argz_(1)-argz_(2)=0`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBJEE 2018|30 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise HS (XI) AND WBJEE 2019 (HS (XI) 2019) (GROUP -A)|10 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise HS (XI) AND WBJEE 2018 (GROUP - C)|17 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

If z_(1)and z_(2) be any two non-zero complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| then prove that, arg z_(1)=arg z_(2) .

If z_1 and z_2 be two non-zero complex numbers such that |z_1+z_2|=|z_1|+|z_2| ,then prove that argz_1-argz_2=0 .

If z_(1),z_(2) are two complex numbers , prove that , |z_(1)+z_(2)|le|z_(1)|+|z_(2)|

z_(1) and z_(2) are two non-zero complex numbers such that z_(1)^(2)+z_(1)z_(2)+z_(2)^(2)=0 . Prove that the ponts z_(1),z_(2) and the origin form an isosceles triangle in the complex plane.

If z_1 and z_2 are non zero complex numbers such that abs(z_1-z_2)=absz_1+absz_2 then

If z_(1)andz_(2) be two non-zero complex numbers such that (z_(1))/(z_(2))+(z_(2))/(z_(1))=1 , then the origin and the points represented by z_(1)andz_(2)

If z_1,z_2 are two non zero complex numbers such that z_1/z_2+z_2/z_1=1 then z_1,z_2 and the origin are

Let z_(1) and z_(2) be any two non-zero complex numbers such that 3|z_(1)|=2|z_(2)|. "If "z=(3z_(1))/(2z_(2)) + (2z_(2))/(3z_(1)) , then

If z_(1)and z_(2) are conjugate complex number, then z_(1)+z_(2) will be

If z_1 and z_2 be two complex numbers such that abs(z_1+z_2)=abs(z_1) +abs(z_2) then the value of argz_1-argz_2 is equal to