Derive the following laws for complex numbers from the corresponding laws for real numbers z 1 z 2 z 2 z 1 , z 1 z 2 z 2 z 1 (Commutative laws) (z 1 z 2 ) z 3 z 1 (z 2 z 3 ), (Associative laws) (z 1 z 2 )z 3 z 1( z 2 z 3 ) z 1 (z 2 z 3 ) z 1 z 2 z 1 z 3 (Distributed laws) 0 z z 0 z, z ( z) ( z) z 0, z 1 z

Question: Derive the following laws for complex numbers from the corresponding laws for real numbers. z 1 + z 2 = z 2 + z 1

Derive the following laws for complex numbers from the corresponding laws for real numbers.

z₁ + z₂ = z₂ + z₁, z₁z₂ = z₂z₁ (Commutative laws)
(z₁ + z₂) + z₃= z₁ + (z₂ + z₃), (Associative laws)
(z₁z₂)z₃= z₁₍z₂z₃)
z₁(z₂ + z₃) = z₁z₂ + z₁z₃ (Distributed laws)
0 + z = z + 0 = z,
z + (-z) = (-z) + z = 0, z · 1 = z.

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