1=cos0+isin0

1+z=(cos0+isin0)+(cos@+isin@)

=(cos@+cos0)+i(sin@+sin0)

=2cos((@+0)/2)cos((@-0)/2)+i(2sin((@+0)/2)cos((@-0)/2)

=2cos^2(@/2)+2isin(@/2)cos(@/2)

mod(1+z)=sqrt((2cos^2(@/2)^2+(2sin(@/2)cos(@/2))^2)

mod(1+z)=sqrt{4cos^(@/2)[cos^2(@/2)+sin^2(@/2)]}

=2cos(@/2)sqrt(cos^2(@/2)+sin^2(@/2))

=2cos(@/2)(1)

=2cos(@/2)