Problem A$.(10$ points$)$ Complex Class In this problem you need to create a class named Complex that models a complex number, numbers of the form x$+$yi$,$ where x and y are real numbers, and i is the imaginary unit equal to the square root of $-1.$ In the x$+$yi representation, we say that x is the real component of the complex number, and y is the imaginary component. Note that Python already has a built$-$in Complex class, but this makes for a good, simple example, so we$$re going to make our own. Obviously, you$$re not allowed to use the built$-$in Complex class to implement your Complex class. Complex objects have two attributes $($also known as instance variables$)$: self.real $($a numeric value representing the real component of the complex number$)$ self.imag $($a numeric value representing the imaginary component$)($Note: Please do not write all of these methods at once. After you have written each method, look for tests below for that method and make sure it$$s working before moving on to the next method$)$ Define a class Complex with the following methods: $\_\_$init$\_\_($self$,$ real, imag$)$: A constructor with two numeric arguments $($not counting self$),$ that initializes the real and imag attributes, respectively. You must have getter and setter methods for both real and imag. They should have the following signatures: get$\_$real$($self$)$ get$\_$imag$($self$)$ set$\_$real$($self$,$ new$\_$real$)$ set$\_$imag$($self$,$ new$\_$imag$)$ Overload the $\_\_$str$\_\_($self$)$ method so that it returns a string of the format: $"+$ i$"$ where and represent the real and imaginary components of the complex number, respectively. Overload the $+$ and $*$ operators, so that they take in a Complex object other, and return a new Complex object representing the sum or product $($respectively$)$ of the complex numbers represented by self and other. See the Hints section if you$$re not familiar with how to add or multiply two complex numbers. You$$ll need to have the following method signatures to overload the operators: $\_\_$add$\_\_($self$,$ other$)\_\_$mul$\_\_($self$,$ other$)$ Overload the $==$ operator, so that it takes in a Complex object other, and returns True if the two objects are equal $($their real components are equal, and their imaginary components are equal$),$ or False otherwise. You$$ll need to have the following method signature to overload the operator: $\_\_$eq$\_\_($self$,$ other$)$ Hints: Review on how to add$/$multiply complex numbers: $($a $+$ bi$)+($c $+$ di$)=($a $+$ c$)+($b $+$ d$)$i $($a $+$ bi$)($c $+$ di$)=($ac $-$ bd$)+($ad $+$ bc$)$i Constraints: You are not permitted to use Python$$s built$-$in Complex class Your methods must have exactly the same names and arguments as described above. Examples: Copy the following if $\_\_$name$\_\_==\text{'}\_\_$main$\_\_\text{'}$ block into your hw$12.$py file. The comment next to each print statement indicates what should be printed out. if $\_\_$name$\_\_==\text{'}\_\_$main$\_\_\text{'}$: x $=$ Complex$(2\mathrm{.}7,3)$ print$($x$.$real$)$ #$2\mathrm{.}7$ print$($x$.$imag$)$ #$3$ print$($x$.$get$\_$real$())$ #$2\mathrm{.}7$ print$($x$.$get$\_$imag$())$ #$3$ x$.$set$\_$real$(8)$ print$($x$)$ #$8+3$i x$.$set$\_$imag$(-4\mathrm{.}5)$ print$($str$($x$)==\text{'}8+-4\mathrm{.}5$i$\text{'})$ #True print$()$ x $=$ Complex$(1\mathrm{.}5,4)$ y $=$ Complex$(-2,0)$ print$($x$+$y$)$ #$-0\mathrm{.}5+4$i print$($x$)$ #$1\mathrm{.}5+4$i print$($y$)$ #$-2+0$i z $=$ Complex$(0,-1\mathrm{.}5)$ print$($z$+$y$+$x$)$ #$-0\mathrm{.}5+2\mathrm{.}5$i print$()$ x $=$ Complex$(6,3)$ z $=$ Complex$(0,-2\mathrm{.}5)$ print$($x$*$z$)$ #$7\mathrm{.}5+-15\mathrm{.}0$i y $=$ Complex$(-4,2)$ print$($x$*$y$)$ #$-30+0$i print$($x$*($y$+$z$))$ #$-22\mathrm{.}5+-15\mathrm{.}0$i print$($x$*$y$*$z$)$ #$0\mathrm{.}0+75\mathrm{.}0$i print$()$ print$($Complex$(4,2)==$ Complex$(4,3))$ #False print$($Complex$(2,6)==$ Complex$(4,6))$ #False print$($Complex$(3,5)==$ Complex$(3,5))$ #True x $=$ Complex$(6,3)$ y $=$ Complex$(-4,2)$ z $=$ Complex$(0,-2\mathrm{.}5)$ print$($x$*$y$+$x$*$z $==$ x$*($y$+$z$))$ #True