Wikipedia here explains it like this:
I understand it so that either $\mu_i=0$ or $g_i=0$ but this answer here:
"If μ1≠0 and μ2≠0, then x is one of the two points at the intersection of the two circles (complementary slackness)"
where I cannot see at all what it has to do with complementary-slackness. Could someone clarify this concept and this example? Please, choose an simpler example if the latter too detailed.
P.s. I am doing the non-linear optimization 2.3139.
You may want to see the video here and at the very end something about complementary-slackness -condition.