Help me start a rogram - Complex nembers

Question

I have an assignment that includes complex numbers, and I have no idea what a complex number is and where to start. Is there anyone that could help me get started?
Program details:
Given a complex number a+ib, we can define the following operations:
* |a+ib| = square root of (a2+b2) is the absolute value operation.
* s(a+ib)=sa+isb, where s is a real number, is scaling.
* the complex conjugate of a+ib is a-ib.
* (a+ib)+(c+id)=(a+c)+i(b+d) is addition.
* (a+ib)*(c+id)=(ac-bd)+i(ad+cb) is multiplication. (Notice that scaling is just a special case, where b=0.)
* do subtraction on your own.
* (a+ib)/(c+id)=((ac+bd)+i(cb-ad))/(c2+d2) is division. You will have to be careful when dividing - the resulting denominator cannot be equal to 0!
You are to write a program which contains two separate files.
The first file will define a Complex class which should include exactly two data members, two constructors, the operations defined above, and a toString method. Important note, the scaling, conjugate, addition, multiplication, subtraction, and division operations all return another complex number. You also must include the appropriate set and get methods. Be sure you comment this class appropriately. Each function should have its own set of comments.
The second file is an application to test your Complex class as follows: repeatedly read numbers of type double (a, b, c, d, and s), create and print the complex numbers a+ib and c+id, print each numbers absolute value, then create and print the following new complex numbers: s(a+ib), the complex conjugate of a+ib, and the sum, product, difference, and quotient of a+ib and c+id. Continue this loop until the user terminates the application.

Answer 1

Yes, learn complex numbers. Java is the least of your problems.
%