For all complex numbers z for which the expressions are defined,  

            [Graphics:Images/ComplexFunTrigMod_gr_57.gif]  

Proof.

    The proof that [Graphics:../Images/ComplexFunTrigMod_gr_58.gif] uses the identity [Graphics:../Images/ComplexFunTrigMod_gr_59.gif]:  

            [Graphics:../Images/ComplexFunTrigMod_gr_60.gif]

We leave the proofs of the other derivative formulas as exercises.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell