Recent content by timeforchg

  1. T

    Cauchy Riemann conditions for analyticity for all values of z.

    SOLVED! Thanks a lot guys! Appreciate it.
  2. T

    Undergrad How do they derive from equation A to B?

    SOLVED! Thanks a lot guys! Appreciate it.
  3. T

    The distinct roots of complex number

    SOLVED! Thanks a lot guys! Appreciate it.
  4. T

    Undergrad How do they derive from equation A to B?

    there is no + in eq A for the denominator
  5. T

    Undergrad How do they derive from equation A to B?

    yes. I think is more simplifying the equation. I am trying to find the limit z = 0. When I see inside my text before they use l'hopital rule, they simplified the equation A to B. Thereafter they apply the l'hopital rule
  6. T

    Undergrad How do they derive from equation A to B?

    My question is how to get from equation A to B. By using partial fractions? differential? any methods?
  7. T

    Cauchy Riemann conditions for analyticity for all values of z.

    Hahaha.. do this by hand?? oh my god! I would suffer from brain damage. ouh well. Ok a quick question. If I need to calculate the derivative of 1/sin(z) at z=0, +- pi/2, +- pi, +-3pi/2... I used quotient rule to get -cos (z)/ sin^2 (z) Thus, sub the values of z into the equation. I will...
  8. T

    Cauchy Riemann conditions for analyticity for all values of z.

    Oopss.. Ok here it goes.. Very nasty.
  9. T

    Cauchy Riemann conditions for analyticity for all values of z.

    It's nasty.. If by theorem, 1/sin(z) will satisfy Cauchy - Riemann conditions for all values of z except z = k pi + pi/2, ( k=0, +- 1, +- 2 ...), where the denominator of the function equals to zero. ??but I try it out manually, it seems it doesn't satisfy the equation. hmm...
  10. T

    Cauchy Riemann conditions for analyticity for all values of z.

    am i right to say that 1/sin (z) in (a+jb) format is sin(x) cosh(y)/ sin^2 (x) cosh^2 (y) + cos^2 (x) sinh^2 (y) - j cos(x) sinh(y)/ sin^2 (x) cosh^2 (y) + cos^2 (x) sinh^2 (y) ?? Correct me if I'm wrong
  11. T

    Cauchy Riemann conditions for analyticity for all values of z.

    Sorry for the mis post.
  12. T

    Cauchy Riemann conditions for analyticity for all values of z.

    thanks for notifying. I mange to solve it. and yes it satifies the condition. What if the equation is 1/sin (z)? I try to conjugate the equation but end up with 0. i guess i did it wrong. How do I start with this equation? Thanks.
  13. T

    Cauchy Riemann conditions for analyticity for all values of z.

    Homework Statement Show that sin(z) satisfies the condition. (Stated in the title) Homework Equations The Attempt at a Solution f(z) = sin (z) = sin (x + iy) = sin x cosh y + i cos x sinh y thus, u(x,y)=sin x cosh y ... v(x,y)= cos x sinh y du/dx = cos x...
  14. T

    The distinct roots of complex number

    Will try it out. Actually, this is not homework. I am just trying out past year exam questions. Sad to say, solutions is not provided. So I will never know whether I am doing it right or wrong.
  15. T

    The distinct roots of complex number

    Hi Simon, Is it possible to show me your method starting from $$z^6-1=\left [ \frac{64j(1-j)}{1+2j} \right ]^6$$ till the end equation $$z^6$$= ##a+jb## please?