Question: is R ^ 2 a vector space over C with respect to the usual addition and the scalar multiplication c ( x , y )

is R ^2a 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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