
Addition of Complex Numbers The sum z_{1} + z_{2} of two complex nujmbers z_{1} = a_{1} + ib_{1} and z_{2} = a_{2} + ib_{2} is defined as the complex number (a_{1} + a_{2}) + i(b_{1} + b_{2}). i.e Closure Property: The sum of two complex numbers is a complex number. Hence, the set of complex numbers is closed under addition.
Commutative Property: For two complex numbers z_{1} = a+ib and z_{2} = c+id, we have
Associative Property: Consider three complex numbers z_{1} = a+ib , z_{2} = c+id, z_{1} = e+if
The Additive Identity: Let a+ib be the identity for addition. Then
Additive Inverse: Let z = a+ib be a complex number and let w = c+id be its additive inverse then
Directions: Answer the following questions. Also write at least 5 examples of each of the property above. 