Please use java A complex number is a number in the form a + b i , 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...

Please use java

A complex number is a number in the form
a
+
b

i
, where
a

and
b
 are real numbers and
i

is√(-1)

The numbersa andb 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 formulas:

a + b
i

+   c + d
i

=  (a+c)+ (b+d)
i


(addition)

a + b
i
−  (c + d
i
)= (a−c) + (b−d)
i


(subtraction)

(a + b
i
)* (c + d
i
)= (ac−bd) + (bc+ad)
i


(multiplication)

(a + b
i
)/ (c + d
i
)= (ac+bd) / (c²+d²) + (bc−ad)
i
/ (c²+d²)
(division)

You can obtain theAbsolute Value for a complex number using the following formula:

|a + b
i
|  =√(a² + b²
)

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 example below.

(1) Design a class named
Complex
 for representing complex numbers

• Include methodsadd,­subtract,multiply,divide, andabs for performing complex-number operations


• OverridetoString method for returning a string representation for a complex number.




• ThetoString method returns(a + b
  
  i
  
  ) as a String.


• Ifb is0, it simply returnsa.




• YourComplex class should also implementCloneable andComparable.




• 
  Compare two complex numbers using their absolute values.
  






•  Provide three Constructors:Complex(
  a, b
  ),Complex(
  a
  ), andComplex().

• 
  Complex() creates aComplex object for number0
  


• 
  Complex(
  a
  ) creates aComplex object with0 forb.

• Also provide thegetRealPart() andgetImaginaryPart() methods for returning the real part and the imaginary part of the complex number, respectively.

(2) Draw the UML class diagram and implement the class.

(3) Write a Test program

• Prompt the user to enter two complex numbers


• Displays the result of their addition, subtraction, multiplication, division, and absolute value.

A sample run is shown below:

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 + 6.5i

(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 + 5.5i)| = 6.519202405202649