Question 317423
Complex numbers are constructions made up of a two real numbers, {{{x}}},{{{y}}}, and an imaginary part,{{{i}}}, in the form,{{{z=x+iy}}}. 
The important property of {{{i}}} is {{{i=sqrt(-1)}}} which makes it useful to solve equations of the form,{{{x^2+a^2=0}}}, among others.  
The solutions for {{{x^2+a^2=0}}} are {{{x=ai}}} and {{{x=-ai}}}.
{{{x^2=-a^2}}}
{{{x^2=(-1)(a^2)}}}
{{{sqrt(x^2)=sqrt((-1)(a^2))}}}
{{{x=0 +- a*sqrt(-1)}}}
{{{x=0 +- ai}}}
There are many application for complex numbers that provide meaningful interpretations in the real world. Search the internet for examples and properties of complex numbers.