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if we're talking about a short dipole, you have {E.H} field depending by r^(-k), where r is distance between antenna's feed and point of {E,H} calculus and k is >=1.

In far field, you can imagine r>>1, so r^(-k) contribution is lower for greater k and you can approximate {E,H} expression by considering only the contribution with the lowest k.

This make Poynting vector become real, according with the assumption that far field radiation power is active, near field one has also a capacitive contribution.

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