An isomorphism from multiplicative group G of nonzero complex number to multiplicative group H = { [ a − b b a ] | a , b ∈ ℝ a n d a 2 + b 2 ≠ 0 } and prove that ϕ ( x + y ) = ϕ ( x ) ⋅ ϕ ( y ) .

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To find: An isomorphism from multiplicative group G of nonzero complex number to multiplicative group H={[a−bba]|a,b∈ℝanda2+b2≠0} and prove that ϕ(x+y)=ϕ(x)⋅ϕ(y).

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