Complex Functions (Differentiability) Show that $f'(z)$ does not exist at any point $z$ when (a) $f(z)=\bar{z}$ (b) $f(z)=Re (z)$ (c) $f(z)=Im (z)$

QUESTION: Show that $f'(z)$ does not exist at any point $z$ when
(a)  $f(z)=\bar{z}$
(b)  $f(z)=Re (z)$
(c)  $f(z)=Im (z)$

APPENDIX: SOME ADDITIONAL SUPPORT FILES.