1.

If (x+y)=(a+bi)²,show that (x²+y²)=(a²+b²)²​

Answer»

Answer:

(a+ i.b)^2 = X + i.y.

or, a^2+ i^2.b^2+ i.2AB = x + i.y.

or, a^2 - b^2 + i. 2ab = x + i. y.

or, Comparing the real and imaginary parts both sides.

x = a^2 - b^2. …………(1).

y = 2ab. …………………..(2)

Squaring and adding both sides the eqn. (1) and (2).

x^2 + y^2 = (a^2 - b^2)^2 +(2ab)^2.

or, x^2 - y^2 = a^4+b^4-2a^2.b^2+ 4a^2b^2 = a^4+b^4+2a^2b^2.

or, x^2 - y^2 = (a^2+b^2)^2. Proved.


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