1、一個復數類Complex由兩部分組成：實部real和虛部imaginary，兩個復數可以進行加減乘除四則運算。
試設計這個復數類，然后在另一個類的程序入口演示。
public class Test {
public static void main(String[] args) {
// 定義兩個對象並賦值：c1(a+bi)=(2+4i),c2=(c+di)=(6+16i)
Complex c1=new Complex();
c1.real=2;
c1.imaginary=4;
Complex c2=new Complex();
c2.real=6;
c2.imaginary=16;
// 以字符串的方式輸出：采用標准格式輸出，即a+bi
System.out.println("兩個復數相加得："+c1.add(c2));
// 在每次調用並運算（此時real值發生變化）之后，再重新賦值：
c1.real=2;
c1.imaginary=4;
System.out.println("兩個復數相減得："+c1.sub(c2));
c1.real=2;
c1.imaginary=4;
System.out.println("兩個復數相乘得："+c1.mul(c2));
c1.real=2;
c1.imaginary=4;
System.out.println("兩個復數相除得："+c1.div(c2));
}
}
class Complex
{
double real;
double imaginary;
//最后以字符串輸出的格式：
//1.虛部為正值時，實部+"+"+虛部+"i" 2.虛部為0時，只有實部，即實部+"" 3.虛部為負值時，實部+""+虛部+"i"
// 加法，減法：直接實部加減實部，虛部加減虛部
String add(Complex c)
{
if(imaginary+c.imaginary>0)
return (real=real+c.real)+"+"+(imaginary=imaginary+c.imaginary)+"i";
else if(imaginary+c.imaginary==0)
return (real=real+c.real)+"";
else
return (real=real+c.real)+""+(imaginary=imaginary+c.imaginary)+"i";
}
String sub(Complex c)
{
if(imaginary-c.imaginary>0)
return (real=real-c.real)+"+"+(imaginary=imaginary-c.imaginary)+"i";
else if(imaginary-c.imaginary==0)
return (real=real-c.real)+"";
else
return (real=real-c.real)+""+(imaginary=imaginary-c.imaginary)+"i";
}
// 乘法的公式：(a+bi)*(c+di) = a*c + bi*c + a*di + bi*di = a*c + (b*d)(i^2) + (b*c+a*d)i
// 注：此處的i^2直接賦值-1，即 return a*c-b*d+(b*c+a*d)i
String mul(Complex c)
{
if(imaginary*c.real+real*c.imaginary>0)
return (real*c.real)-(imaginary*c.imaginary)+"+"+(imaginary*c.real+real*c.imaginary)+"i";
else if(imaginary*c.real+real*c.imaginary==0)
return (real*c.real)-(imaginary*c.imaginary)+"";
else
return (real*c.real)-(imaginary*c.imaginary)+""+(imaginary*c.real+real*c.imaginary)+"i";
}
// 除法的公式：(a+bi)/(c+di) = (a+bi)*(c-di) / c^2+d^2
// 注：在乘法的基礎上得到格式A+Bdi，再進行A /c^2+d^2，B /c^2+d^2 + "i"
String div(Complex c)
{
if(imaginary*c.real-real*c.imaginary>0)
return ((real*c.real)+(imaginary*c.imaginary))/(c.real*c.real+c.imaginary*c.imaginary)+"+"+(imaginary*c.real-real*c.imaginary)/(c.real*c.real+c.imaginary*c.imaginary)+"i";
else if(imaginary*c.real-real*c.imaginary==0)
return ((real*c.real)+(imaginary*c.imaginary))/(c.real*c.real+c.imaginary*c.imaginary)+"";
else
return ((real*c.real)+(imaginary*c.imaginary))/(c.real*c.real+c.imaginary*c.imaginary)+""+(imaginary*c.real-real*c.imaginary)/(c.real*c.real+c.imaginary*c.imaginary)+"i";
}
}
/*Complex c1=new Complex();
c1.real=2;
c1.imaginary=4;
Complex c2=new Complex();
c2.real=6;
c2.imaginary=16;
即：c1=2+4i
c2=6+16i
數學運算結果：
兩者相加：8+20i
兩者相減：-4-12i
兩者相乘：-52+56i
(2+4i)*(6+16i)
兩者相除：0.2602739726027397-0.0273972602739726i
(2+4i)/(6+16i)=(2+4i)*(6-16i)/(6*6+16*16)*/