Building Complex Systems

Any systems which involves a quantity of elements, set in structures which can subsist on a lot of scales is called the complex systems. These leave during processes of modify that are not describable by a solitary regulation nor are reducible to single stage of details, these levels often include features whose appearance cannot be predicted from their present specifications. Complex Systems speculation also includes the study of the connections of the a lot of parts of the systems.

Building complex systems:

            The complex number is specify the Z = a + ib
            The imaginary number is called as the tetragon root of a negative number. It is specify the `sqrt(-a)`  a > 0 is an imaginary number.
            The real numbers are a and b. The complex number is called as the a+ib. The real part is called a and imaginary part is called b.
Types of building complex system
            The first type is equality of complex numbers. The second type is calculation of two complex numbers. The third type is negative of a complex number. The fourth type is preservative identity of the complex number. The fifth type is preservative inverse of a complex number. The sixth type is creation of two complex numbers. The last type is multiplicative individuality of complex numbers.
Properties of building complex system
            There are a lot of propertied of the building complex system.  
            The first property is the commutative law for calculation.   
            The second property is Commutative Law for increase.
            The third property is Additive character Exists.
            The fourth property is Multiplicative character Exist.
            The fifth property is Reciprocals Exist for nonzero complex numbers.
            The sixth property is Negatives be real for every complex numbers.
            The last property is Non Zero invention Law.

Example problem of building complex systems:

Problem 1 :
`sqrt(-64)`
Solution
        `sqrt(-64)`
     =  `sqrt(64(-1))`
     =`sqrt(64)sqrt(-1)`
     = 8i
Problem 2:
          `-sqrt(-81)`
Solution
     = `-sqrt(-81)` 
     = `-sqrt(81(-1))`
     = `-sqrt(81)sqrt(-1)`
     =-9i