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'''Arithmetic with complex number''' refers to simple operations mathematicians perform on a [[complex number]]. The motivating factor for the use of complex numbers is that they form an [[algebraically closed]] [[Field_(mathematics)|field]]. In simpler language any [[algebraic]] [[operation]] that is performed on a complex number gives a complex number. This is not true for [[real number]]s, for example, <math>x^{2}+1=0</math> is an entirly real expression but <math>x</math> cannot be a real number. The solution is <math>x=\pm i</math>.

'''Arithmetic with complex number''' refers to simple operations mathematicians perform on a [[complex number]]. The motivating factor for the use of complex numbers is that they form an [[algebraically closed]] [[Field_(mathematics)|field]]. In simpler language any [[algebraic]] [[operation]] that is performed on a complex number gives a complex number. This is not true for [[real number]]s, for example, <math>x^{2}+1=0</math> is an entirly real expression but <math>x</math> cannot be a real number. The solution is <math>x=\pm i</math>.