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Consider C as a vector space over R in the natural way. Here vector addition and...

Consider C as a vector space over R in the natural way. Here vector addition and scalar
multiplication are the usual addition and multiplication of complex numbers. Show that {1 − i, 1 + i} is
linearly independent. Consider C as a vector space over C in the natural way. Here vector addition is the
usual addition of complex numbers and the scalar multiplication is the usual multiplication of a real number
by a complex number. Show that {1 − i, 1 + i} is not linearly independent.

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