



 
Hi Douglas, I assume that $a$ and $b$ are real and then \[0^{a + bi} = 0^a \times 0^{bi}.\] If $a \neq 0$ then $0^a = 0$ and hence \[0^{a + bi} = 0^a \times 0^{bi} = 0 \times 0^{bi} = 0 \] If $a=0$ then $a+bi = bi$ and hence \[0^{a + bi} = 0^{bi} \mbox { which is undefined.}\] Hence if $a$ and $b$ are real then \[0^{a + bi} = \left\{ \begin{array}{ll} 0 & \mbox{if $a \neq 0$} \\ \mbox{ undefined} & \mbox{ if $a = 0$} \end{array} \right.\] Penny 



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