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