537. Complex Number Multiplication

这道题主要是实现复数的乘法(主要是实现题目的特殊要求)
利用string.split(“\+”)将字符串“+”分开得到复数的实部和虚部
(a1+a2*i)*(b1+b2*i)=(a1*b1-a2*b2)+(a1*b2+a2*b1)*i,但是当结果为负数时候,有特殊的形式“+-”,所以需数要进行判断正负,具体代码如下:

public String complexNumberMultiply(String a, String b) {
        String[] A=a.split("\\+");
        String[] B=b.split("\\+");
        int a1=Integer.parseInt(A[0]);
        int a2=Integer.parseInt(A[1].replace("i", ""));
        int b1=Integer.parseInt(B[0]);
        int b2=Integer.parseInt(B[1].replace("i", ""));
        int re=a1*b1-a2*b2;
        int im=a1*b2+a2*b1;
        StringBuffer sb=new StringBuffer();
        sb.append(re);
        sb.append("+");
        if (im<0) {
            sb.append("-"+Math.abs(im));
        }else {
            sb.append(Math.abs(im));
        }
        sb.append("i");
        return sb.toString();
    }
1. Problem Description: A complex number is a number of the form a +bi, where a and b are real numbers and i is √-1 The numbers a and b are known as the real part and imaginary part of the complex number, respectively. You can perform addition, subtraction, multiplication, and division for complex numbers using the following formula: a+bi+c+di=(a+c)+(b+d)i a+bi-(c+di)=(a-c)+(b-d)i 第2页共2页 (a+bi)*(c+di)=(ac-bd)+(bc+ad)i (a+bi)/c+di)=(ac+bd)/c²+d²)+(bc-ad)i/(c²+d²) You can also obtain the absolute value for a complex number using the following formula: latbil=√a²+b (A complex number can be interpreted as a point on a plane by identifying the (a, b) values as the coordinates of the point. The absolute value of the complex number corresponds to the distance of the point to the origin, as shown in Figure 13.12b.) Design a class named Complex for representing complex numbers and the methods add, subtract, multiply, divide, abs for performing complex-number operations, and override toString method for returning a string representation for a complex number. The toString method returns a + bi as a string. If b is 0, it simply returns a. Provide three constructors Complex(a, b), Complex(a), and Complex(). Complex() creates a Complex object for number 0 and Complex(a) creates a Complex object with 0 for b. Also provide the getRealPart() and getlmaginaryPart() methods for returning the real and imaginary part of the complex number, respectively. Your Complex class should also implement the Cloneable interface. Write a test program that prompts the user to enter two complex numbers and display the result of their addition, subtraction, multiplication, and division. Here is a sample run: <Output> Enter the first complex number: 3.5 5.5 Enter the second complex number:-3.5 1 (3.5 + 5.5i) +(-3.5 + 1.0i)= 0.0 + 6.5 (3.5 + 5.5i)-(-3.5 + 1.0i)= 7.0 + 4.5i (3.5 + 5.5i)*(-3.5 + 1.0i) =-17.75 +-15.75i (3.5 + 5.5i) /(-3.5 + 1.0i)=-0.5094 +-1.7i |3.5 + 5.5il = 6.519202405202649 <End Output>
06-09
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