Modern Math CNthRoot

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CNthRoot

Returns any one of the n nth roots of a complex number.

Syntax

CNthRoot( byref z as Complex, byval n as int32, byval k as int32 = 0 ) as Complex

Notes

• Gives you all the roots, not just the principal one. k = 0 is the principal root and k = 1 … n-1 are the others, spaced 2π/n apart around the same circle. Nothing else in the docset does this.
• Every one of them, raised to the n-th power, reproduces the operand.
• n = 0 gives CNaN( ); there is no zeroth root.
• From AfxNova.

Examples

#import "std/numeric"
using numeric

dim as Complex z = CSet( 3, 4 )

print CToString( CNthRoot( z, 3, 0 ) )  '' 1.628937145922176+0.5201745023045459i   -- the principal cube root
print CToString( CNthRoot( z, 3, 1 ) )  '' -1.2649529063577518+1.1506136983844504i   -- the second
print CToString( CNthRoot( z, 3, 2 ) )  '' -0.3639842395644245-1.6707882006889965i   -- the third
print CIsNaN( CNthRoot( z, 0, 0 ) )     '' true

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