CVT2

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Verify the identity: \sin(iz) = i\sinh(z)\,

\sin(iz)\, = \frac{e^{i(iz)} - e^{-i(iz)}}{2i}
= \frac{e^{-z} - e^{z}}{2i}
= \frac{i}{i}\cdot\frac{e^{-z} - e^{z}}{2i}
= -i\cdot\frac{e^{-z} - e^{z}}{2}
= i\cdot\frac{e^{z} - e^{-z}}{2}
= i\sinh{z}\,


Main Page : Complex Variables : Trigonometric Functions

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