if a+ib = (x+i)square /2x square +1.prove that a square +b square =(x square +1) square /(2x square +1) square
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Answers
Answer:
a+ib= (x+I)^2/2x^2+1
using (a+b)^2=a^2+b^2+2ab
= (x^2+i^2+2xi)/(2x^2+1)
put i^2= -1,
= (x^2-1)/(2x+1)+i (2x)/(2x^2+1)
comparing real part
a=xsquare-1/2xsquare+1
comparing imaginary p....
b=2x/2xsquare+1
calculating .. a square+b square
a square+b square =( x square-1/2x square+1)Square +(2x/2x Square+1)Square
=(x Square-1) Square+(2x)Square/(2x Square+1) Square
Using (a-b)^2= a square+b square-2an
=(x square)Square+1 square-2(x square)1+4x square/ (2x square+ 1)2
= x^4+1-2x square+4x square/(2x square+2) Square
= x^4+1+2x square/(2x square+1)Square
(x^2) Square+(1 )square+2x square (1)
..' a square + b square =( x Square+1) Square/(2x Square+1 ).
Step-by-step explanation:
a+ib= (x+I)^2/2x^2+1
using (a+b)^2=a^2+b^2+2ab
= (x^2+i^2+2xi)/(2x^2+1)
put i^2= -1,
= (x^2-1)/(2x+1)+i (2x)/(2x^2+1)
comparing real part
a=xsquare-1/2xsquare+1
comparing imaginary p....
b=2x/2xsquare+1
calculating .. a square+b square
a square+b square =( x square-1/2x square+1)Square +(2x/2x Square+1)Square
=(x Square-1) Square+(2x)Square/(2x Square+1) Square
Using (a-b)^2= a square+b square-2an
=(x square)Square+1 square-2(x square)1+4x square/ (2x square+ 1)2
= x^4+1-2x square+4x square/(2x square+2) Square
= x^4+1+2x square/(2x square+1)Square
(x^2) Square+(1 )square+2x square (1)
..' a square + b square =( x Square+1) Square/(2x Square+1 ).