What is the additive identity of the complex number 14 + 5i?
A) 14 – 5i
B) 0
C) 1
D) –14 – 5i
The correct answer and explanation is:
The correct answer is B) 0.
In the context of complex numbers, the additive identity is the number that, when added to any complex number, leaves that complex number unchanged. This number is 0 in the complex number system.
A complex number consists of two parts: a real part and an imaginary part. The given complex number is 14 + 5i, where 14 is the real part and 5i is the imaginary part. The additive identity for complex numbers is the number 0 + 0i, which means the real part is 0, and the imaginary part is also 0.
When you add 0 + 0i to any complex number, the result is the original complex number itself. For example:
(14 + 5i) + (0 + 0i) = 14 + 5i
This operation shows that adding the additive identity (0) to a complex number does not change the number.
Looking at the other options:
- A) 14 – 5i is not the additive identity because adding it to the original complex number would change the real and imaginary parts, resulting in a new number, not the original one.
- C) 1 is not the additive identity, because adding 1 to a complex number would change its real part, and it is not a valid additive identity for complex numbers.
- D) –14 – 5i is also incorrect, as adding this number would drastically change both the real and imaginary parts of the original number.
Thus, the additive identity for any complex number is always 0.