The Addition Of Two Squares Identity?

$\Rightarrow (x+yi)(x-yi)$

$=x^2-(yi)^2$

$=x^2+y^2$

$\Rightarrow (x+yi)(x-yi)=x^2+y^2$

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Note: $i^2=-1$ .

Difference formula is ( x - y)(x + y) = x^2 - y^2.
Iota equals Under-root -1.
Option . ( x - iy )( x + iy ).
= x( x + iy ) -iy( x + iy )
= x^2 + xyi -xiy - (iy)^2 :- i^2 = -1
= x^2 - (-1)(y)^2
= x^2 + y^2
It shows ( x - iy )( x + iy ) is correct option. For further feel free to inbox me. :)

$x^{2}+y^{2}$ $=x^{2}-(-y^{2})$ $=x^{2}-(-1) \times y^{2}$ $=x^{2}-i^{2} \times y^{2}$ $=x^{2}-(yi)^{2}$ $=(x+yi)(x-yi)$ Hence, the answer is $\boxed{(x+yi)(x-yi)}$