Title Description:

The complex number can be written as the general form of (A+Bi)(A+Bi)(A+Bi) (a + bi) (a + bi), in which AAA is the real part, BBB is the virtual part, I I I is the unit of imaginary number, satisfying I2 = − 1i^2 = − 1i2 = − 1i2 = − 1i2 = − 1i2 = − 1i2 = − 1; or the exponential form under polar coordinates (R × e (Pi) (R × e ^ {(Pi)} (Pi)) (R × e (Pi)), in which R is the complex modulus, P is the radiation angle, I is the unit of imaginary number, its equivalence, its equivalence, its equivalent, P is the radiation angle, I is the unit of imaginary number, its equivalent, its equivalence, its equivalent, its imaginary number unit in trigonometry Form (R(cos(P)+isin(P))(R(cos(P)+isin(P))(R(cos(P)+isin(P)).

Given the R and P of two complex numbers, it is required to output the normal form of the product of two numbers.

Input format:

Input two complex numbers R1,P1,R2,P2 1, p 1, R 2, P 2 R1,P1,R2,P2 in a row, separated by spaces.

Output format:

In one line, the normal form of the product of two numbers is output according to the format of A+Bi. Both the real part and the virtual part retain two decimal places. Note: if B is a negative number, it should be written as A-|B|i.

Input example:

2.3 3.5 5.2 0.4

Output example:

-8.68-8.23i

Code example (Java implementation)

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner cin = new Scanner(System.in);

        double a0 = cin.nextDouble();
        double b0 = cin.nextDouble();
        double c0 = cin.nextDouble();
        double d0 = cin.nextDouble();

        double a = a0 * Math.cos(b0);
        double b = a0 * Math.sin(b0);
        double c = c0 * Math.cos(d0);
        double d = c0 * Math.sin(d0);

        double i = (a * c - b * d);
        double j = (a * d + b * c);

        /**
         * There is a little pit when processing the calculation results.
         * For real part: if the result after decimal point processing is: - 0.00, it needs to be converted to 0.00.
         * For the imaginary part: if the result after the decimal point is: - 0.00i, it needs to be converted to + 0.00i.
         * In fact, I have some doubts about this transformation, because in fact, the sign of the calculation result itself is a negative number.
         * It's smaller than 0, and when it turns out like this, it's not a negative number.
         * But if we only see five in one, we can understand it again.
         * Hee hee
         */
        String result = String.format("%.2f", i);
        if ("-0.00".equals(result)) {
            result = "0.00";
        }
        
        String result1 =  j >= 0 ? (String.format("+%.2fi", j)) : (String.format("%.2fi", j));
        if ("-0.00i".equals(result1)) {
            result1 = "+0.00i";
        }
        System.out.println(result + result1);
    }

}