complex variable

hi, im just a little bit stuck on this question. Use the definition of the derivative of a function to prove that the funtion f(z)=Im z is nowhere differentiable.
i know that f'(z)=lim f(z+delta(z))-f(z)/delta(z)
along the real axis, ive found the limit to be 1, bt along the imaginary axis ive also found this to be the case, so can anyone tell me where ive gone wrong.

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Originally Posted by joker1

hi, im just a little bit stuck on this question. Use the definition of the derivative of a function to prove that the funtion f(z)=Im z is nowhere differentiable.
i know that f'(z)=lim f(z+delta(z))-f(z)/delta(z)
along the real axis, ive found the limit to be 1, bt along the imaginary axis ive also found this to be the case, so can anyone tell me where ive gone wrong.

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Along the real axis you should find that the limit is 0, because the imaginary part of a number does not change if you add a real number to it.