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Algebra

Cool goIITian

 Joined: 31 Dec 2007 Post: 35
15 Jan 2008 10:39:54 IST
0 People liked this
1
431
PLEAZ SOLVE IT FULLY...............
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

FOR ANY 2 COMPLEX NUMBERS Z1 ,Z2 ZND REAL NUMBERS A AND B  ,
THEN WHAT IS |AZ1 - BZ2|2  +  |BZ1 + AZ2|2  ....

Hot goIITian

Joined: 10 Jan 2008
Posts: 107
15 Jan 2008 20:29:47 IST
4 people liked this

similarly,

|Az1 - Bz2|^2  = (A^2) z1^2 + (B^2) z2^2 - 2Re(ABz1z2(bar))

and

|Bz1 + Az2|^2 = (B^2) z1^2 + (A^2) z2^2 + 2Re(ABz1z2(bar))

=>  |Az1 - Bz2|^2  +  |Bz1 + Az2|^2
= (A^2) z1^2 + (B^2) z2^2 + (B^2) z1^2 + (A^2) z2^2

=  (A^2) (z1^2 + z2^2) + (B^2) (z1^2 + z2^2)

= ((A^2) + (B^2)) (z1^2 + z2^2)      ANS

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