The multiplicative identity of any number, including complex numbers, is the number that when multiplied by the original number does not change its value. For all real and complex numbers, this identity is 1.
In the case of the complex number 4 + 8i, if we multiply it by the multiplicative identity (which is 1), it remains unchanged:
(4 + 8i) × 1 = 4 + 8i
This property holds true for all complex numbers:
- 0 is not the multiplicative identity, as any number multiplied by 0 equals 0.
- 1 is the identity element for multiplication, ensuring that we can always get back our original complex number.
Therefore, the multiplicative identity of the complex number 4 + 8i is simply 1.