Can you tell me, if i am eating 1000 calories a day and burning 1000 calories will i lose 4lbs a week?

No: If you burn what you eat, your weight will never change.

Depends on weight: Wow! You are really going for some weight loss here! The answer to your question actually depends on your weight! Maybe! Four pounds a week of fat is actually quite a lot to lose in one week! Getting ready for an event? Trying to lose weight after a baby? Beware that severe calorie restriction like this will make your body go into " starvation mode" increasing stress hormones to conserve fat!

Unlikely: However it would depends on many other factors. Usually you can take in a little more than you burn in calories to maintain a healthy body. A 1000 calorie diet cannot be sustained and you would be better off with a slower and less drastic program for long-term benefits or may end up even much heavier once the dieting is over.