Page 27 - Calculus with Complex Numbers
P. 27
Ffgure 2.8
Ffgure 2. 7
For complex variables however it turns out that trigonometric functions
and hyperbolic functions are intimately related. The following formulae are
fundamental for all that follows.
2.6 Fundam ental form ulae
For all real .x we have
sintïar) = i sinh .z7 ,
sinhtïar) = i sin .x,
costïar) = cosh .z7
coshtïx) = cos x.
These formulae can be proved in several ways. For example by delinition
from Huler's formulae for sin.x cos .x (see Section 1.8).
