/**
* Calculates the cosine (cosinus) of {@link BigComplex} x in the complex domain.
*
* @param x the {@link BigComplex} to calculate the cosine for
* @param mathContext the {@link MathContext} used for the result
* @return the calculated cosine {@link BigComplex} with the precision specified in the <code>mathContext</code>
*/
public static BigComplex cos(this BigComplex x, MathContext mathContext)
{
MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode());
return(BigComplex.valueOf(
BigDecimalMath.cos(x.re, mc).multiply(BigDecimalMath.cosh(x.im, mc), mc).round(mathContext),
BigDecimalMath.sin(x.re, mc).multiply(BigDecimalMath.sinh(x.im, mc), mc).negate().round(mathContext)));
}
/**
* Calculates the natural exponent of {@link BigComplex} x (e<sup>x</sup>) in the complex domain.
*
* <p>See: <a href="https://en.wikipedia.org/wiki/Exponential_function#Complex_plane">Wikipedia: Exponent (Complex plane)</a></p>
*
* @param x the {@link BigComplex} to calculate the exponent for
* @param mathContext the {@link MathContext} used for the result
* @return the calculated exponent {@link BigComplex} with the precision specified in the <code>mathContext</code>
*/
public static BigComplex exp(this BigComplex x, MathContext mathContext)
{
MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode());
BigDecimal expRe = BigDecimalMath.exp(x.re, mc);
return(BigComplex.valueOf(
expRe.multiply(BigDecimalMath.cos(x.im, mc), mc).round(mathContext),
expRe.multiply(BigDecimalMath.sin(x.im, mc), mc)).round(mathContext));
}
/**
* Calculates {@link BigComplex} x to the power of {@link BigDecimal} y (x<sup>y</sup>).
*
* @param x the {@link BigComplex} value to take to the power
* @param y the {@link BigDecimal} value to serve as exponent
* @param mathContext the {@link MathContext} used for the result
* @return the calculated x to the power of y with the precision specified in the <code>mathContext</code>
*/
public static BigComplex pow(this BigComplex x, BigDecimal y, MathContext mathContext)
{
MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode());
BigDecimal angleTimesN = x.angle(mc).multiply(y, mc);
return(BigComplex.valueOf(
BigDecimalMath.cos(angleTimesN, mc),
BigDecimalMath.sin(angleTimesN, mc)).multiply(BigDecimalMath.pow(x.abs(mc), y, mc), mc).round(mathContext));
}
/**
* Returns a complex number with the specified polar {@link BigDecimal} radius and angle using the specified {@link MathContext}.
*
* @param radius the {@link BigDecimal} radius of the polar representation
* @param angle the {@link BigDecimal} angle in radians of the polar representation
* @param mathContext the {@link MathContext} used to calculate the result
* @return the complex number
*/
public static BigComplex valueOfPolar(BigDecimal radius, BigDecimal angle, MathContext mathContext)
{
if (radius.signum() == 0)
{
return(ZERO);
}
return(valueOf(
radius.multiply(BigDecimalMath.cos(angle, mathContext), mathContext),
radius.multiply(BigDecimalMath.sin(angle, mathContext), mathContext)));
}