Q. 54.9( 9 Votes )

Show that

(i) is purely real,

(ii) is purely real.

Answer :

Given:

Taking the L.C.M, we get




[(a + b)(a – b) = (a2 – b2)]




Putting i2 = -1




= 0 + 0i


Hence, the given equation is purely real as there is no imaginary part.


(ii) Given:


Taking the L.C.M, we get



…(i)


[(a + b)(a – b) = (a2 – b2)]


Now, we know that,


(a + b)2 + (a – b)2 = 2(a2 + b2)


So, by applying the formula in eq. (i), we get




Putting i2 = -1






Hence, the given equation is purely real as there is no imaginary part.


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