Question: Let C* = C{0} be the set of non-zero complex numbers, and let GL(2, R) denote the set of 2 x 2 invertible matrices with

$Let C* = C\\{0} be the set of non-zero complex$

Let C* = C\\{0} be the set of non-zero complex numbers, and let GL(2, R) denote the set of 2 x 2 invertible matrices with real entries. You may assume that C* with complex multiplication, and GL(2, R) with matrix multiplication, are both groups. (i) Define d : C* - GL(2, R) by p(x tiy) = Show that o is a homomorphism. (ii) Show that a -b H = a, bER, a2 + 62 0 a is a subgroup of GL(2, ). (iii) Show that C* is isomorphic to H

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