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$\lim_{\Delta z \to 0} \frac{\frac{-1}{\bar{z_0} + \Delta z \bar{\Delta z} + z_0 \bar{\Delta z} + \bar{z_0} \Delta z} - \frac{-1}{|z_0|^2}}{\Delta z}$ \newline let $\Delta z = 0 + iy$ \newline Notice that when delta z approaches zero on the \newline imaginary axis, we may represent z bar as negative \newline delta z. \newline $\lim_{\Delta z \to 0} \frac{\frac{-1}{\bar{z_0} - \Delta z \bar{\Delta z} - z_0 \bar{\Delta z} + \bar{z_0} \Delta z} - \frac{-1}{|z_0|^2}}{\Delta z}$ \newline Similarly, when delta z approaches zero from the real axis, \newline we may represent delta z bar as just delta z. \newline $\lim_{\Delta z \to 0} \frac{\frac{-1}{\bar{z_0} + \Delta z \bar{\Delta z} + z_0 \bar{\Delta z} + \bar{z_0} \Delta z} - \frac{-1}{|z_0|^2}}{\Delta z}$

          $\lim_{\Delta z \to 0} \frac{\frac{-1}{\bar{z_0} + \Delta z \bar{\Delta z} + z_0 \bar{\Delta z} + \bar{z_0} \Delta z} - \frac{-1}{|z_0|^2}}{\Delta z}$ \newline let $\Delta z = 0 + iy$ \newline Notice that when delta z approaches zero on the \newline imaginary axis, we may represent z bar as negative \newline delta z. \newline $\lim_{\Delta z \to 0} \frac{\frac{-1}{\bar{z_0} - \Delta z \bar{\Delta z} - z_0 \bar{\Delta z} + \bar{z_0} \Delta z} - \frac{-1}{|z_0|^2}}{\Delta z}$ \newline Similarly, when delta z approaches zero from the real axis, \newline we may represent delta z bar as just delta z. \newline $\lim_{\Delta z \to 0} \frac{\frac{-1}{\bar{z_0} + \Delta z \bar{\Delta z} + z_0 \bar{\Delta z} + \bar{z_0} \Delta z} - \frac{-1}{|z_0|^2}}{\Delta z}$

limΔ z → 0((-1)/(z̅0̅ + Δ z Δ̅ ̅z̅ + z0 Δ̅ ̅z̅ + z̅0̅Δ z) - (-1)/(|z0|^2))/(Δ z) let Δ z = 0 + iy Notice that when delta z approaches zero on the imaginary axis, we may represent z bar as negative delta z. limΔ z → 0((-1)/(z̅0̅ - Δ z Δ̅ ̅z̅ - z0 Δ̅ ̅z̅ + z̅0̅Δ z) - (-1)/(|z0|^2))/(Δ z) Similarly, when delta z approaches zero from the real axis, we may represent delta z bar as just delta z. limΔ z → 0((-1)/(z̅0̅ + Δ z Δ̅ ̅z̅ + z0 Δ̅ ̅z̅ + z̅0̅Δ z) - (-1)/(|z0|^2))/(Δ z)

Added by Michael M.

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