identity crisis is a much discussed topic. what is identity complex? can anyone please enlighten me about this?

I believe an identity crisis is when someone loses themself to the point they no longer know who they are.
but another type would be when the person has an identical twin or has found someone who looks exactly like them down to their mannerisms and way of talking.
dont quote me but I believe there is also the mid-life crisis which is a crisis of identity.
sometimes multiple personality disorder is reffered to this way as well.
if you think you are having one go to a psychiatrist or therapist immediately.
A serious crisis of identity can effect your everyday life especially if blackouts, memory loss or amnesia is present. hope this helps, but like I said a doctor or a trained professional would be the go to for this sort of thing.

are identity crisis and identity complex similar? is it so?

usually yes, if you have a complex it is usually the sign of a crisis.
A complex could also be a multiple personality complex or even an identity problem with past lives.
again if you or someone you know is having difficulties do not hesitate to talk with someone who is trained in these sorts of things.
psychiatrist, therapist and past life regression hypnotist to name a few. sometimes a crisis is easily solved if treated soon enough.
a persons shadow side or self can cause this sort of problem as well.
for a shadow problem try to find a therapist who is well versed in jungian archetypes or cognitive therapy.