If two real vectors/signals are orthogonal, then are their associated complex vectors/signals also orthogonal?

Question

Being Z1 and Z2 two complex vectors/signals with N samples; X1 and X2 the correspondent real signals with (2N + 1) samples.

Is it true that if X1 and X2 are orthogonal, then are Z1 and Z2 also orthogonal? If Z1 and Z2 are orthogonal, then are X1 and X2 also orthogonal?

Answer 1

Consider $Z_1=(i,1,0)$ and $Z_2=(1,-i,0)$ for the first case.

Consider $Z_1=(1,-i,0)$ and $Z_2=(1,i,0)$ for the second case.