import?java.util.objects;

public?class?Complex?{

	?private?final?double?re;???//?the?real?part
	????private?final?double?im;???//?the?imaginary?part

	????//?create?a?new?object?with?the?given?real?and?imaginary?parts
	????public?Complex（double?real?double?imag）?{
	????????re?=?real;
	????????im?=?imag;
	????}

	????//?return?a?string?representation?of?the?invoking?Complex?object
	????public?String?toString（）?{
	????????if?（im?==?0）?return?re?+?““;
	????????if?（re?==?0）?return?im?+?“i“;
	????????if?（im?	????????return?re?+?“?+?“?+?im?+?“i“;
	????}

	????//?return?abs/modulus/magnitude
	????public?double?abs（）?{
	????????return?Math.hypot（re?im）;
	????}

	????//?return?angle/phase/argument?normalized?to?be?between?-pi?and?pi
	????public?double?phase（）?{
	????????return?Math.atan2（im?re）;
	????}

	????//?return?a?new?Complex?object?whose?value?is?（this?+?b）
	????public?Complex?plus（Complex?b）?{
	????????Complex?a?=?this;?????????????//?invoking?object
	????????double?real?=?a.re?+?b.re;
	????????double?imag?=?a.im?+?b.im;
	????????return?new?Complex（real?imag）;
	????}

	????//?return?a?new?Complex?object?whose?value?is?（this?-?b）
	????public?Complex?minus（Complex?b）?{
	????????Complex?a?=?this;
	????????double?real?=?a.re?-?b.re;
	????????double?imag?=?a.im?-?b.im;
	????????return?new?Complex（real?imag）;
	????}

	????//?return?a?new?Complex?object?whose?value?is?（this?*?b）
	????public?Complex?times（Complex?b）?{
	????????Complex?a?=?this;
	????????double?real?=?a.re?*?b.re?-?a.im?*?b.im;
	????????double?imag?=?a.re?*?b.im?+?a.im?*?b.re;
	????????return?new?Complex（real?imag）;
	????}

	????//?return?a?new?object?whose?value?is?（this?*?alpha）
	????public?Complex?scale（double?alpha）?{
	????????return?new?Complex（alpha?*?re?alpha?*?im）;
	????}

	????//?return?a?new?Complex?object?whose?value?is?the?conjugate?of?this
	????public?Complex?conjugate（）?{
	????????return?new?Complex（re?-im）;
	????}

	????//?return?a?new?Complex?object?whose?value?is?the?reciprocal?of?this
	????public?Complex?reciprocal（）?{
	????????double?scale?=?re*re?+?im*im;
	????????return?new?Complex（re?/?scale?-im?/?scale）;
	????}

	????//?return?the?real?or?imaginary?part
	????public?double?re（）?{?return?re;?}
	????public?double?im（）?{?return?im;?}

	????//?return?a?/?b
	????public?Complex?divides（Complex?b）?{
	????????Complex?a?=?this;
	????????return?a.times（b.reciprocal（））;
	????}

	????//?return?a?new?Complex?object?whose?value?is?the?complex?exponential?of?this
	????public?Complex?exp（）?{
	????????return?new?Complex（Math.exp（re）?*?Math.cos（im）?Math.exp（re）?*?Math.sin（im））;
	????}

	????//?return?a?new?Complex?object?whose?value?is?the?complex?sine?of?this
	????public?Complex?sin（）?{
	????????return?new?Complex（Math.sin（re）?*?Math.cosh（im）?Math.cos（re）?*?Math.sinh（im））;
	????}

	????//?return?a?new?Complex?object?whose?value?is?the?complex?

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2018-12-14?15:17??Test\
?????文件?????????377??2019-01-02?17:39??Test\.classpath
?????文件?????????380??2018-12-14?15:17??Test\.project
?????目錄???????????0??2018-12-14?15:17??Test\.settings\
?????文件?????????598??2018-12-14?15:17??Test\.settings\org.eclipse.jdt.core.prefs
?????目錄???????????0??2019-01-03?17:24??Test\bin\
?????文件????????4456??2019-01-03?17:24??Test\bin\Complex.class
?????文件????????3114??2019-01-03?17:24??Test\bin\FFT.class
?????目錄???????????0??2019-01-02?17:39??Test\src\
?????文件????????4920??2019-01-02?17:31??Test\src\Complex.java
?????文件????????6807??2019-01-02?18:50??Test\src\FFT.java