# Question #9cb16

##### 1 Answer

#### Answer:

Any convergent sequence of real numbers will converge to a real number.

#### Explanation:

If we look at the question directly as asked, then the answer is yes, as the real numbers are a subset of the complex numbers. Then, any convergent sequence of reals will converge to a complex number.

Assuming, however, that the question is asking whether there can be a sequence of real numbers which converge to a number with an imaginary component, the answer is no.

A sequence

Suppose

This shows directly that given any proposed limit with an imaginary component, we can demonstrate that the sequence does not converge to that limit by setting