At this point, we are ready to start using our $`$Sandwich$`$ class objects!

$**$Solve it$!**$

Create your own $``$ComplexNumber$``$ class in the cell with the comment $`$#si$-$complex$-$number$`!$

$1.$ Complex numbers have a real and an imaginary part. The $`\_\_$init$\_\_()`$ method should therefore accept two numbers. Store the first as self.real and the second as self.imag.

$2.$ Implement a $`$conjugate$()`$ method that returns the object's complex conjugate $($as a new $`$ComplexNumber$`$ object$).$ Recall that $x $=$ a $+$ bi $\backslash$implies $\backslash$bar$\{$x$\}=$ a $-$ bi$$,$ where $$\backslash$bar$\{$x$\}$$ is the complex conjugate of $x$$.$

$3.$ Add the following magic methods to your $`$ComplexNumber$`$ class:

$-`\_\_$abs$\_\_()`$ determines the output of the builtin $`$abs$()`$ function $($absolute value$).$ Implement $`\_\_$abs$\_\_()`$ so that it returns the magnitude of the complex number. Recall that $$|$a $+$ bi$|=\backslash$sqrt$\{$a$^2+$ b$^2\}$$$.$

$-$ Implement $`\_\_$lt$\_\_()`$ and $`\_\_$gt$\_\_()`$ so that $`$ComplexNumber$`$ objects can be compared by their magnitudes. That is$,$ $$($a $+$ bi$)<($c $+$ di$)$$ if and only if $$|$a $+$ bi$|<|$c $+$ di$|$$$,$ and so on$.$

$4.$ Add the following magic methods to your $`$ComplexNumber$`$ class:

$-$ Implement $`\_\_$eq$\_\_()`$ and $`\_\_$ne$\_\_()`$ so that two $`$ComplexNumber$`$ objects are equal if and only if they have the same real and imaginary parts.

$-$ Implement $`\_\_$add$\_\_()`,`\_\_$sub$\_\_()`,`\_\_$mul$\_\_()`,$ and $`\_\_$div$\_\_()`$ appropriately. Each of these should return a new $`$ComplexNumber$`$ object.