|

Algebra

Cool goIITian

 Joined: 1 Dec 2007 Post: 50
13 Jan 2008 20:59:32 IST
0 People liked this
1
486
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

if  Iz1+z2I= Iz1I -Iz2I then arg z1 - arg z2=?

ans= pi

Hot goIITian

Joined: 10 Jan 2008
Posts: 107
13 Jan 2008 21:32:27 IST
5 people liked this

Sudakar,

z1, z2 r 2 complex numbers on z-plane, |z1| and |z2| represent modulus (magnitude) of z1 n z2.

|z1 + z2| is again a complex number on same plane.

z1, z2 and z1+z2 will make a triangle,

in triangle, difference of any two side is greater than third side.
=> |z1| - |z2| > |z1 + z2|

but |z1| - |z2| = |z1 + z2| is given => z1, z2, z1+z2 don't make a triangle. they are in one line.

Now if they are on the same side of origin, obviously |z1 +  z2| = |z1| + |z2|
but we have, |z1 +  z2| = |z1| - |z2|
=> z1 and z2 must be on the different side of origin.
=> if we rotate line of z1 by pi-angle we get line of z2.

=> arg z1 - arg z2 = pi

 Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a avatar to have your pictures show up by your comment If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

For Quick Info

Name

Mobile

E-mail

City

Class

Find Posts by Topics

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 9960 m Post - 2185
4. edison
 Altitude - 10815 m Post - 7797
5. Sagar Saxena
 Altitude - 8625 m Post - 8064