In simple mathematics, division indicates the ratio between two numbers a' and b'. So, any number when divided by zero has been termed undefined to prevent arguments and complications. However, in complex mathematics division by zero is possible.
When, a number is multiplied with zero, it yields zero. So, if the inverse of the number is taken it comes to an undefined fraction of 0/0. This fraction has not been resolved nor argued by mathematicians since centuries.
But, let us take a case where 1 is divided by zero and an absurd number U' is the result. So, U multiplied by zero and then multiplied by two, results into two. As, U being the inverse of zero when multiplied with zero becomes 1 and 1 multiplied with two results into two, which is the law of multiplication. Thus, there lies a definition that division by zero can be possible; however the context is not with real or imaginary numbers but with an absurd number defined as U.
This argument can be further justified by the anomaly of squares and square roots. When, two negative numbers are multiplied it gives to a positive number. So, it is not possible to have a square root of a negative number. So, mathematicians had to come up with complex numbers which had imaginary number i', as a multiplication factor to the square root of the negative number. Thus, the complex number has a real and an imaginary part. The imaginary part of the rational number has its importance in practical calculations of electrical engineering.
So, how does the absurd number has its existence? Philosophically, what exists' is question that has to be defined. When, we think of love, hate or other emotions, we know it is there but there is no physical definition to these feelings. Two people can show different variations of love which cannot be defined by laws or rules. A mother and a son would love each other in a different way than the same son with his newly wed wife. Similarly, we also know that God is omnipresent but we have no physical evidence or a proof of His existence.
Sometimes it is transitional of something's existence and a possibility of the existence in a particular domain. Division of zero is not possible in a real and imaginary number system but, in absurd mathematics it is possible to divide zero and get a number. This fact is strengthened more with extended complex plane and calculus. The L'Hospital Rule in calculus also describes the functionality of division by zero within a particular limit. In extended complex plane, the factor 1/0 has been termed as complex infinity.
Finally, the concept of absurd numbers and division by zero should be limited within a particular domain of absurd numerical. In real or imaginary number system, these numbers or the concept might not find a place but in other domains it is possible.