Ex-5 – i) Mark the complex number on the Argand Plane ii) Determine the Real Part, Imaginary Part, Conjugate, Modulus and Argument [Given Complex number Z = 4 + 3i]

\[\text{Do the following}\ \hspace{25cm}\]

\[1.\ \text{To mark the given complex number z on the Argand Plane.}\ \hspace{15cm}\\ \text{To find the real and imaginary parts of z.}\ \hspace{18cm}\\ \text{To find the distance of z from y – axis and related it to the imaginary part of z.}\ \hspace{10cm}\]

\[2.\ \text{To find the conjugate of z.}\ \hspace{22cm}\\ \text{Mark}\ \bar{z}\ \text{on the Argand Plane.}\hspace{16cm}\\ \text{Find the reflection of z, on x-axis and relate it to} \bar{z}.\ \hspace{15cm}\]

\[3.\ \text{To find the modulus of z.}\ \hspace{22cm}\\ \text{Find the distance between z and origin of the Argand plane and relate it to the modulus of z.}\ \hspace{8cm}\\ \text{Find the modulus of}\ \bar{z}\ \text{and related it to the modulus of z}\ \hspace{15cm}\]

\[4.\ \text{To find the argument of z.}\ \hspace{22cm}\\ \text{Find the angle between the line segment Oz and x axis and relate it to the argument of z.}\ \hspace{8cm}\\ \text{Find the argument of}\ \bar{z}\ \text{and related it to the argument of z}\ \hspace{15cm}\]

\[\color{green}{Step\ 1:}\ \text{Open Geogebra classic 5 (by double clicking on the icon)}\ \hspace{18cm}\]

\[\color{green}{Step\ 2:}\ \text{To plot the complex number z = 4 + 3i}\ \hspace{18cm}\\ \text{by using the input bar to type}\ z_1\ =\ 4\ +\ 3i\ \text{and press the Enter key}\ \hspace{14cm}\]

\[\color{green}{Step\ 3:}\ \text{To find the real and imaginary part of the given complex number}\ \hspace{18cm}\\ \text{by using the input command}\ R\ =\ real(z_1)\ and\ I\ =\ imaginary(z_1)\ \text{and press the Enter key}\ \hspace{14cm}\]

\[\color{green}{Step\ 4:}\ \text{To plot the origin}\ \hspace{22cm}\\ \text{by using the input bar to type}\ 0\ =\ (0,0)\ \hspace{20cm}\]

\[\color{green}{Step\ 5:}\ \text{To find the point of intersection on x axis,}\ \hspace{18cm}\\ \text{by using the Perpendicular line tool and then intersect tool}\ \hspace{14cm}\]

\[\color{green}{Step\ 6:}\ \text{Similarly, to find the point of intersection on y axis,}\ \hspace{18cm}\\ \text{by using the Perpendicular line tool and then intersect tool}\ \hspace{14cm}\\ \text{and hide the lines f and g by using algebra view}\ \hspace{16cm}\]

\[\color{green}{Step\ 7:}\ \text{To find the distance from O to A}\ \hspace{22cm}\\ \text{by using the input command OA = Segment(O,A),}\ \hspace{14cm}\\ \text{distance of the segment appears in the algebra view named as OA}\ \hspace{14cm}\]

\[\color{green}{Step\ 8:}\ \text{Similarly, to find the distance from O to B}\ \hspace{22cm}\\ \text{by using the input command OB = Segment(O,B),}\ \hspace{14cm}\\ \text{distance of the segment appears in the algebra view named as OA}\ \hspace{14cm}\]

\[\color{green}{Step\ 9:}\ \text{To find the conjugate of the given complex number}\ z_1\ \hspace{18cm}\\ \text{by using the input command}\ z_2\ =\ conjugate(z_1)\ \text{and press the Enter key}\ \hspace{14cm}\]

\[\color{green}{Step\ 10:}\ \text{To find the reflection of the given complex number}\ z_1\ \hspace{18cm}\\ \text{by using the input command}\ z_3\ =\ Reflect(z_1, xAxis)\ \text{and press the Enter key}\ \hspace{14cm}\]

\[\color{green}{Step\ 11:}\ \text{To find the modulus of the given complex number}\ z_1\ \hspace{18cm}\\ \text{by using the input command}\ M\ =\ abs(z_1)\ \text{and press the Enter key}\ \hspace{14cm}\]

\[\color{green}{Step\ 12:}\ \text{To find the distance between the origin and the given complex number}\ z_1\ \hspace{12cm}\\ \text{by using the input command D = Segment(O,z_1)}\ \text{and press the Enter key}\ \hspace{14cm}\]

\[\color{green}{Step\ 13:}\ \text{To find the distance between the origin and the given complex number}\ z_2\ \hspace{12cm}\\ \text{by using the input command D = Segment(O,z_2)}\ \text{and press the Enter key}\ \hspace{14cm}\]

\[\color{green}{Step\ 14:}\ \text{To find the argument of the given complex number}\ z_1\ \hspace{14cm}\\ \text{by using the input command arg(z_1)}\ \text{and press the Enter key}\ \hspace{14cm}\]

\[\color{green}{Step\ 15:}\ \text{To find the angle between the given complex number}\ z_1\ \text{and x axis}\ \hspace{12cm}\\ \text{by using the input command Angle(A,O,z_1)}\ \text{and press the Enter key}\ \hspace{14cm}\]

\[\color{green}{Step\ 16:}\ \text{To find the argument of the given complex number}\ z_2\ \hspace{14cm}\\ \text{by using the input command arg(z_2)}\ \text{and press the Enter key}\ \hspace{14cm}\]

\[\color{green}{Step\ 17:}\ \text{To create an input box for Z and link with}\ z_1\ \hspace{18cm}\]