Expert: Ahmed Salami - 3/2/2006

Question
prove that (z=a+bi,absolute value z-zconjugate)=2b

Answer
Hi Lacey,
If z = a + bi
The conjugate of z is defined as
z' = a - bi
And so
z - z' = (a + bi) - (a - bi)
      = a + bi - a + bi
      = 2bi
The absolute value of the complex number z = a + bi is
sqrt(a^2 + b^2)
But z - z' = 0 + (2b)i
Its absolute value if therefore
sqrt[0^2 + (2b)^2]
= sqrt(4b^2)
= 2b

I hope i have helped you. You can always get back to me.
Regards.