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Algebra

Cool goIITian

Joined:	31 Dec 2007
Post:	35

15 Jan 2008 10:39:54 IST

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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 _^....

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Rohit Gupta

Hot goIITian

Joined: 10 Jan 2008

Posts: 107

15 Jan 2008 20:29:47 IST

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See this : http://www.goiit.com/posts/list/algebra-want-answer-with-steps-38778.htm

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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