public BigComplex Sqrt(MathContext mc)
{
BigDecimal half = new BigDecimal(2);
/* compute l=sqrt(re^2+im^2), then u=sqrt((l+re)/2)
* and v= +- sqrt((l-re)/2 as the new real and imaginary parts.
*/
BigDecimal l = Abs(mc);
if (l.CompareTo(BigDecimal.Zero) == 0)
{
return(new BigComplex(BigMath.ScalePrecision(BigDecimal.Zero, mc),
BigMath.ScalePrecision(BigDecimal.Zero, mc)));
}
BigDecimal u = BigMath.Sqrt(l.Add(Real).Divide(half, mc), mc);
BigDecimal v = BigMath.Sqrt(l.Subtract(Real).Divide(half, mc), mc);
if (Imaginary.CompareTo(BigDecimal.Zero) >= 0)
{
return(new BigComplex(u, v));
}
else
{
return(new BigComplex(u, v.Negate()));
}
}
public BigDecimal Abs(MathContext mc)
{
return(BigMath.Sqrt(Norm(), mc));
}