Home
Class 12
MATHS
If z1,z2 and z3,z4 are two pairs of conj...

If `z_1,z_2` and `z_3,z_4` are two pairs of conjugate complex numbers then `arg(z_1/z_4)+arg(z_2/z_3)=`

A

0

B

`(pi)/(2)`

C

`pi`

D

`(3pi)/(2)`

Text Solution

Verified by Experts

Promotional Banner

Similar Questions

Explore conceptually related problems

If z_(1), z_(2) and z_(3), z_(4) are two pairs of conjugate complex numbers, then find arg ((z_(1))/(z_(4)))+arg((z_(2))/(z_(3))) .

If z_1 and z_2 , are two non-zero complex numbers such tha |z_1+z_2|=|z_1|+|z_2| then arg(z_1)-arg(z_2) is equal to

Let z_(1),z_(2) and z_(3) be three non-zero complex numbers and z_(1) ne z_(2) . If |{:(abs(z_(1)),abs(z_(2)),abs(z_(3))),(abs(z_(2)),abs(z_(3)),abs(z_(1))),(abs(z_(3)),abs(z_(1)),abs(z_(2))):}|=0 , prove that (i) z_(1),z_(2),z_(3) lie on a circle with the centre at origin. (ii) arg(z_(3)/z_(2))=arg((z_(3)-z_(1))/(z_(2)-z_(1)))^(2) .

If z_1 and z_2 are two complex number such that |(z_1-z_2)/(z_1+z_2)|=1 , Prove that iz_1/z_2=k where k is a real number Find the angle between the lines from the origin to the points z_1 + z_2 and z_1-z_2 in terms of k

z_(1) and z_(2) are two complex number such that |z_(1)|=|z_(2)| and arg (z_(1))+arg(z_(2))=pi , then show that z_(1)=-barz_(2)

State true of false for the following: Let z_(1) and z_(2) be two complex number's such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| then arg (z_(1)-z_(2))=0

Consider z_(1)andz_(2) are two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| Statement -1 arg (z_(1))-arg(z_(2))=0 Statement -2 The complex numbers z_(1) and z_(2) are collinear.

If z and we are two complex numbers such that |zw|=1 and arg(z)-arg(w)=(pi)/(2) then show that barzw=-i

If arg (z) lt 0 then arg(-z)-arg(z) =.....

Let z and w are two non zero complex number such that |z|=|w|, and Arg(z)+Arg(w)=pi then (a) z=w (b) z=overlinew (c) overlinez=overlinew (d) overlinez=-overlinew