The set of Complex numbers (C) with addition:

Option C

A complex number can be written in the form a + bi where a and b are Real numbers and
i = √(-1)

•  If a + bi ∈ C, (a + bi) + (0 + 0i)  = a + bi is always true, so (0 + 0i)  is the identity element.

• If a + bi ∈ C, (a + bi) + (-a − bi) = 0 + 0i and (-a − bi) + (a + bi) = 0 + 0i  (the identity element), so (a + bi) and (-a − bi) are inverses of each other.

• For any three complex numbers (a₁ + b₁i), (a₂ + b₂i) and (a₃ + b₃i) in C:
(a₁ + b₁i) + [(a₂ + b₂i) + (a₃ + b₃i)] = [(a₁ + b₁i) + (a₂ + b₂i)] + (a₃ + b₃i)
⇒ The associative law has been followed.

• If (a₁ + b₁i) and (a₂ + b₂i) are any two Complex numbers:
(a₁ + b₁i) + (a₂ + b₂i) = (a₁ + a₂) + (b₁ + b₂)i, which is also a Complex number.
⇒ The closure law has been followed.

Therefore, all four conditions for a group are followed by the set C under addition.
⇒ C is a group with respect to addition.