Complex number : A complex number is a number of the form $a+bi$ with real numbers $a,b$ and $i=\sqrt{-1}$ being the imaginary unit. Two complex numbers can be added by adding their real parts and imaginary parts separately. For example $(2+3i)+(4+5i)=6+8i.$ One can multiply two complex numbers by using the distributive property of multiplication and sorting terms taking into account that $i^2=-1.$ For example $(1+2i)(3+4i)$ $=1\cdot 3+1\cdot 4i+2i\cdot 3+2i\cdot 4i$ $=3+4i+6i-8$ $=-5+10i.$ The fundamental theorem of algebra states that a polynomial of degree $n$ has exactly $n$ complex numbers as roots.