# Thread: Another HARD complex question

1. ## Another HARD complex question

Need to do these by tomorrow morning. Any last minute help welcome. Cheers

Which of the following functions are holomorphic at z=0? Prove your answer
A) lzlsquared
B)Re(z) + Im(z)
C)Re(z).Im(z)

2. Originally Posted by sg2004
Need to do these by tomorrow morning. Any last minute help welcome. Cheers

Which of the following functions are holomorphic at z=0? Prove your answer
A) lzlsquared
B)Re(z) + Im(z)
C)Re(z).Im(z)
(C) has been done in this recent thread, it is equivalent to problem (b) there.

RonL

3. Originally Posted by sg2004
B)Re(z) + Im(z)
f(x+i y) = x+y

does not satisfy the Cauchy-Riemann equations at z=0.

(du/dx=1, but dv/dy=0)

RonL

4. Originally Posted by sg2004
A) lzlsquared
Is not holomorphic at z=0, as though it satisfies the Cauchy-Riemann
equations there, it does not satisfy them at any other point, so it is
not complex differentiable in any neighbourhood of 0.

RonL

5. Thanks so much Capn Black.... Cheers!