Alg6.1.4

From Exampleproblems

Solve $(ix+iy)^2\,$

Expanding $((ix)^{2})+2(ix)(iy)+((iy)^{2})\,$

$((i)^{2}(x^{2})+2(i^{2}(xy))+((i)^{2}(y^{2})\,$

Substituting the value of $i^2=-1\,$ in the above we get $(-1)(x^{2})+2(-1)(xy))+(-1)(y^{2})\,$

$-x^{2}-2xy-y^{2}\,$

Taking minus common in the above, $-(x^{2}+2xy+y^{2})\,$

The solution is $-(x+y)^{2}\,$