Why can't we add and subtract complex numbers when they are in polar form,
and multiply and divide complex numbers when they are in rectangular form?
Specially when we work electrical circuits problems.....?

 

We can multiply and divide complex numbers in rectangular form. Where did you get the idea that you can't? In polar form adding or subtracting magnitudes and angles produces a meaningless result. What we want is the vector sum or difference and the rules of vector algebra must be followed.