Modulus of a Complex number

For, z = a + bi , the modulus is
|z| = sqrt(a^2 + b^2)

e.g, 
z = (1 + 2i)^2
z = (1 + 2i) . (1 + 2i)
  = 1 + 2i + 2i + 4i^2    (remember that, i^2 = -1 )
  = 1 + 4i + 4(-1)
  = -3 + 4i


|z| = sqrt( -3^2 + 4^2)
    = sqrt(9 + 16)
    = sqrt(25)
|z| = 5