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chapter complex number if x-iy=(a-ib) 1/2 /(c-id) 1/2 , then prove that (x 2 +y 2 ) 2 = (a 2 +b 2 )/(c 2 +d 2 )

chapter complex number
if x-iy=(a-ib)1/2/(c-id)1/2, then prove that (x2+y2)2 = (a2+b2)/(c2+d2)

Grade:11

2 Answers

Arun
25750 Points
4 years ago
Dear student 
 
conjugate: x+iy = sqrt(a+ib)/(c+id)
 
Now multiply both complex number
 
x^2 + y^2 = sqrt (a^2 +b^2) /sqrt (c^2 + d^2)
 
hence
(x^2 + y^2)^2 = (a^2 +b^2)/ (c^2 + d^2)
Vikas TU
14149 Points
4 years ago
Dear student 
(x+iy ) (x-iy) 
expand using (a+b)(a-b) formula. 
=> (x^2 + y^2)
x-iy=(a-ib)1/2/(c-id)1/2 (Given ) …...1 
Then 
x+iy=(a+ib)1/2/(c+id)1/2..................2
Multiply 1 and 2 
we will get 
x2 + y2 = (a2+b2)/(c2+d2)
Hope this helps 
Good luck
 
 
 

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