Modern Math CExp

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CExp

Returns e raised to a complex power.

Syntax

CExp( byref z as Complex ) as Complex

Notes

• exp( re ) scaled by cos( im ) and sin( im ) — that is, a rotation by the imaginary part and a scale by the real one.
• On the real axis the answer is exactly real. Going through cos/sin would leave rounding dust in the imaginary part where zero belongs, so that case is answered directly.
• Euler's identity holds: CExp( i·π ) is -1.
• Spelled with the C prefix because, when this library was a header in namespace FB, Exp there shadowed the intrinsic for every later header — measured, it broke what is now random.tiko. The name stayed when the header became std/numeric.

Examples

#import "std/numeric"
using numeric

print CToString( CExp( CZero( ) ) )       '' 1+0i
print CToString( CExp( CSet( 1, 0 ) ) )   '' 2.718281828459045+0i   -- exactly real
print CToString( CExp( CSet( 0, PI ) ) )  '' -1+1.2246063538223773e-016i   -- Euler, to within rounding
print CToString( CExp( CSet( 3, 4 ) ) )   '' -13.128783081462158-15.200784463067954i

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Library: Math Library
Category: Math Library
Documented under: Members