|Addition of Complex Numbers|
The sum z1 + z2 of two complex nujmbers z1 = a1 + ib1 and z2 = a2 + ib2 is defined as the complex number (a1 + a2) + i(b1 + b2). 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 z1 = a+ib and z2 = c+id, we have
Associative Property: Consider three complex numbers z1 = a+ib , z2 = c+id, z1 = 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.