sinh/cosh of complex number on TI-89

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Is there another way of calculating sinh(1+j) for example instead of decomposing in sin and cos?

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I am curious what will show up here.

My view is that the direct definition is in terms of the exponential function: $$ \sinh(x+iy) = \frac{e^{x+iy} - e^{-(x+iy)}}{2} $$ so unless your exponential function is ready for complex arguments, you will at some point have to evaluate $e^{ix}$ and there use cosine and sine.