Homework $\backslash$#$5$

$1.$ Write a Java program that implements and tests the following interface for complex numbers:

Test your class with the following main program:

$```$

public static void main$($String$[]$ args$)\{$

Complex x $=$ new Complex$(-5\mathrm{.}0,4\mathrm{.}0)$;

Complex y $=$ new Complex$(3\mathrm{.}0,-2\mathrm{.}0)$;

Complex sum $=$ x$.$plus$($y$)$;

Complex prod $=$ y$.$times$($x$)$;

Complex power $=$ x$.$pow$(4)$;

System.out.println$($x$)$;

System.out.println$($y$)$;

System.out.println$($sum$)$;

System.out.println$($prod$)$;

System.out.println$($power$)$;

System.out.println$($x$.$isReal$())$;

System.out.println$($y$.$norm$())$;

$\}//$ end of test program

$```$

Turn in a listing of your program, and the results of the test run.

$($Note: the methods plus and times do not mutate the complex number, but rather produce a new complex number as the result.$)$

Extra Credit: Add a method norm$()$ that returns the Euclidean norm of the complex number. Test it by printing the norm of $\backslash ($ y $\backslash ).($Hint: the squareroot function is Math.sqrt$($t$).)$