Create a package named Q$2.$

Create a new Java class called ComplexNumber as shown in the UML diagram.

Specifications for the ComplexNumber Class $($In combination with the UML$)$:

The constructor without argument will assign zero to all the field values.

The Constructor with parameters: should accept the real and imaginary values

as arguments and assign these values to the fields $($real and imaginary$).$

Define the accessor$/$getter methods only; no mutator$/$setter methods are required. The getMagnitude$()$ method is a helper method which will return the magnitude of

Lab Exercise $05$ a complex number. Magnitude of a complex number: a$+$bi $=!+!($Use

Math.pow$()$ and Math.sqrt$()$ methods$)$

$$ The getAngle$()$ method is a helper method which will return the angle of a complex number in degrees. Angle of a complex number $($a$+$bi$)$ is tan$"$# $ $($Here$,$ i is a symbol

$"$# $ $\%$

for the imaginary part of the number. For tan $\%$ use Java$$s Math class

Math.atan$2($b$,$ a$)$ that returns the angle in radians, and use Math.toDegrees$($x$)$ method to convert the radians to degrees. You can use these two in nested form. See Unit $2,$ Part $5.($All the trigonometric methods in the Math class return the results in radians, and to get the result in degrees one must use Math.toDegree$($x$)$ method$)$

$$ The displayRecForm$()$ method will display the complex number as shown in the sample output. For example, if the complex number is $($a $+$ bi$),$ it should display a $+$ bi with the corresponding a and b values. The i in the display needs to be hard coded as a literal. The displayed result should use up to $2$ decimal places.

$3.$ In the same Java package, create a driver class with the name:

ComplexNumberDemoYourFirstName.

Import the Q$1.$StudentGradesByYourFirstName class at the top so that you can use your myHeader$()$ and myFooter$()$ methods from that class in the same way, you did in your last lab.

This class will contain two public static fields $-$ a Scanner type instantiated field, and an int type field with an initial value $0,$ and four public$-$static methods $$ dataEntry$(),$ complexAdder$(),$ complexMultiplier$()$ and main$().$

a$)$ Specifications for dataEntry$()$ method:

o Theheader:publicstaticComplexNumberdataEntry$()$

o Oncecalled,insidethemethod,itwillincrementtheintegertypefieldyou

declared. We use it to keep the track of the number of Complex numbers in a

run. You can see in the sample output that it says complex number $1,2$ etc. o Thenitwillprompttheusertoentertherealandimaginarypartsofa

complex number. Get those with the help of the Scanner type data field you

already declared in this class.

o Atthispoint,itwilldeclareaComplextNumbertypereferencevariableand

instantiate it with the above values.

o Finally,itwillreturntheaboveinstantiatedreferencevariablebacktothe

calling method.

b$)$ Specifications for complexAdder$()$ method:

o Theheader:

public static ComplexNumber complexAdder $($ComplexNumber x$,$

ComplexNumber y$)$

o Oncecalled,itwilldeclareanewComplexNumbertypereferencevariableand instantiate it with the added real$-$term values of x and y$,$ and the added imaginary$-$term values of x and y$.$

Note: If there are two complex numbers x $=$ a $+$ bi$,$ and y $=$ c $+$ di$,$ then, x $+$ y $=($a $+$ c$)+($b $+$ d$)$ i$.$

Example: if there are two complex number x $=5+2$i and y $=43$i$,$ then, x $+$ y $=(5+4)+(2-13)$i $=911$i$.$

o Itwillreturntheaboveinstantiatedreferencevariablebacktothecalling method.

Page $6$ of $8$

ES$1036$B $-$ Programming Fundamentals for Engineers

c$)$ Specifications for complexMultiplier$()$ method:

Lab Exercise $05$

Note: Run the program three times as per the following cases. The output should appear as the

following Sample Outputs. To test your code with more data$-$points, use the following website

$($the result may vary slightly in the decimal points while you are comparing, and that is fine$)$:

https:$//$www$.$omnicalculator.com$/$math$/$cartesian$-$to$-$polar

Run$1$:

o Theheader:

public static ComplexNumber complexMultiplier $($ComplexNumber x$,$ ComplexNumber y$)$

o Oncecalled,itwilldeclareanewComplexNumbertypereferencevariable and instantiate it with the appropriate values that result from the multiplication of x and y$.$

Note: If there are two complex numbers x $=$ a $+$ bi$,$ and y $=$ c $+$ di$,$ then, x $*$ y $=($ac $-$ bd$)+($bc $+$ ad$)$ i

o Itwillreturntheaboveinstantiatedreferencevariablebacktothecalling method.

d$)$ Specifications for the Driver Method:

o CallmyHeader$()$inthesamewayasyoudidforQ$2$inyourpreviouslab. o DeclareaComplexNumbertypereferencevariablex.

o CallthedataEntry$()$methodandassignthereturnedvaluetoxdeclared

above.

o RepeatthesameprocedureforasecondComplexNumbertypereference

variable y$.$

o Displaythetwocomplexnumbersusingthea$+$biformasshowninthe

sample output using the displayRecForm$()$ method.

o Declarea$3$rdcomplexreferencevariablecalledaddRes.

o CallthecomplexAdder$()$methodwiththereferencevariablesxandyas

arguments, and then assign the returned value to addRes.

o Declarea$4$thcomplexreferencevariablecalledmulRes.

o CallthecomplexMultiplier$()$methodwiththereferencevariablesxandy

as arguments, and then assign the returned value to