 A number of the form x + iy is called a complex number. x is called the real part and y is called the imaginary part. x and y belong to R. The value of i = √(1). x = Re(x + iy) and y = Im(x + iy)
 If z = x + iy and x = 0 then we call z purely imaginary and if y = 0 then we call z purely real.
 If z = x + iy then complex conjugate of z is con(z)and con(z) = x  iy. Re(con(z)) = Re(z) and Im(con(z)) =  Im(z)
 Polar representation of z = x + iy is z = r (cos θ + i sin θ).
r = √(x^{2} + y^{2}), r is called the modulus of z.
θ = tan^{1} (y/x), θ is called the argument of z. We denote it as Arg z.
De Moivre's Theorem
 De Moivre's Theorem states e^{inθ} = cos (nθ) + i sin (nθ) for any n∈Z and any angle θ.
 We can conclude using De Moivre's theorem that [r (cos θ + i sin θ)]^{n} = r^{n} [cos (nθ) + i sin (nθ)]
 Uses of De Moivre's Theorem
 It can be used to find and prove trigonometrical identities.
 It can be used to find roots of a complex number.
 The three cube roots of unity are 1,ω,ω^{2} where ω = (1 + i√3)/2
