is R $^2$a vector space over C with respect to the usual addition and the scalar multiplication c $($ x $,$y $)=($ cx $,$cy $),$c e C $?$What if it is instead defined as c $($ x $,$ y $)=($ ax $,$by $),$c $=$ a $+$ bi $,$for a $,$ b e R $?$

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To determine if the set R2 is a vector space over C with respect to the given operations we check th... View the full answer