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    we have three complex number Z1,Z2,Z3  =      (a₁+b₁) ,  ( c₁ ,d₁ ) , (e₁  , f₁ )     ∈  ℂ THEN law of distribution addition over multiplication                         (a₁, b₁) .[  ( c₁ ,d₁ ) + (e₁  , f₁ )]  =    (a₁, b₁).  ( c₁ ,d₁ ) +  (a₁, b₁) . (e₁  , f₁ )     L.H.S        =       (a₁, b₁) .[  ( c₁ ,d₁ ) + (e₁  , f₁ )]     LEFT IAW OF DISTRIBUTION                                                 =    (a₁, b₁) (    c₁ + e₁ , d₁+ f₁ )                                   multiplication property of two numbers in complex number                                        = [ a₁ (  c₁ + e₁) -  b₁(  d₁+ f₁) , a₁ ( d₁+ f₁ ) +   b₁(   c₁ + e₁ ) ] by multiplying                                        =  a₁  c₁ + a₁ e₁ -  b₁  d₁ -  b₁  f₁     ,     a₁ d₁+ a₁  f₁  +   b₁   c₁ + b₁   e₁......................1       R.H.S         =       (a₁, b₁) .  ( c₁ ,d₁ ) +  (a₁, b₁) . (e₁  , f₁ )   RIGHT LAW OF DISTRIBUTION                                                       multiplication property in c

 IOTA  describes   the real quantity of complex form to solve complex number equation and equation may be trigonometry, algebra equation, quadric equation and any equation of complex number   mathematically IOTA  denoted by the sign  I or  ι  complex number Z  =  a +bi   where a and b are real number  iota is the imaginary  POWER OIOTA   when the power of iota change it describes the real number and complex number , usually real value of  IOTA  is    ι =  √⁻1 POWER OF IOTA IN DIAGRAM //// CUBE ROOT OF UNITY POWER? solve iota power EXAMPLE  if  we   find the iota power 8 SOLUTION                                   ᵢ⁸ = (ᵢ₄)² =(1)²=1     any power of iota divided by 4 to             EXAMPLE: 2                                    solve     ι⁹ SOLUTION                                                ι⁹  =        ι × ι⁸                                            =     ι ×( ι⁴ )²                                            =    ι × (1)2                                             =    ι × 1  

DEFINITION OF UNION The set of all elements of SET A and SET B is called the union of sets where repeating element eliminates symbolically we denote the sign " U  union of two set A and B is denoted by the sign AUB says set of all element A and B Words union mean together and we read AUB A union B AUB = { set of all elements, such that, all elements of A and B } mathematically we write AUB = { y: y is part of A or part of B } if we have set A = { 1,2,3,4,5,6,7 } and B = { 5,6,7,8,9 } AUB ={ 1,2,3,4,5,6,7 } U { 5,6,7,8,9 } AUB = { 1,2,3,4,5,6,7,8,9 } A U B diagram is shown as we take an example to more explanation Example 1 :   if we have set S = { 15,16 ,17,20,25} T = { 12, 13,14 }   S U T = { 12,13,14,15,16,17,20,25} Example 2   R = { 0,1,7,9,11.17 } and S = { 5,7,,11,15 }     R U S = { 0.1,7,9,11,15,17 }           we cannot repeat element in union of set EXAMPLE 3     if we have P se