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==Transcendency==
The function {{math|''e''<sup>''z''</sup>}} is
If {{math|''a''<sub>1</sub>, ..., ''a''<sub>''n''</sub><nowiki/>}} are distinct complex numbers, then {{math|''e''<sup>''a''<sub>1</sub>''z''</sup>, ..., ''e''<sup>''a''<sub>''n''</sub>''z''</sup><nowiki/>}} are linearly independent over <math>\C(z)</math>, and hence {{math|''e''<sup>''z''</sup>}} is [[transcendental function|transcendental]] over <math>\C(z)</math>.
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