Is the Euclidean Metric on RxR and C a Valid Metric?

[fabbi007]

R is real line, C is set of Complex numbers

If we considered the Euclidean metric on RXR

a. Show whether the Euclidean metric on R
RXR is a metric.
b. Show whether the Euclidean metric on C
C is a metric.
c. Generalize the Euclidean metric to a set made up of all n-tuples of real numbers
X=R power n. Is this also true on C power n?

Can I get some direction on solving this proofs?

 

[g_edgar]

a. Show whether the Euclidean metric on RxR is a metric.

There is a definition for "metric". Check all 3 clauses of that definition in this particular case.