Modern Math CPow

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CPow

Raises a complex or real number to a complex or real power.

Syntax

CPow( byref z as Complex, byref w as Complex ) as Complex
CPow( byref z as Complex, byval p as float64 ) as Complex
CPow( byval x as float64,  byref w as Complex ) as Complex

Notes

• The ^ operator resolves to this in all three arrangements.
• Two answers here are .NET's and are wrong, and they are pinned by a test rather than quietly corrected. CPow( 0, 0 ) is 1 — the zero-exponent test comes first — and CPow( 0, w ) is 0 for every other w, including negative w, where the true answer is infinite. Kept for source compatibility with both of this header's sources; changing it should be a deliberate act.
• For a non-zero base it is exp( w · log z ) evaluated in polar form, so it inherits CLog's branch cut.
• CPow( z, 0.5 ) and CSqrt( z ) agree; CSqrt is the more accurate of the two.

Examples

#import "std/numeric"
using numeric

print CToString( CPow( CSet( 3, 4 ), 2.0 ) )        '' -6.999999999999998+24.000000000000004i
print CToString( CSet( 3, 4 ) ^ 2.0 )               '' -6.999999999999998+24.000000000000004i   -- the operator agrees
print CToString( E ^ CSet( 0, PI ) )                '' -1+1.2246063538223773e-016i   -- Euler again, through the operator
print CToString( CPow( CZero( ), CSet( -1, 0 ) ) )  '' 0+0i   -- pinned: .NET's answer, and wrong

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