Given
Points on a graph.
Find
a) identify the points and find the distance between them.
b) complex conjugate of second point.
c) find z2 - z1
Explanation
a) as we see from the graph , points are
[tex]\begin{gathered} z_1=(3,5) \\ z_2=(6,-3) \end{gathered}[/tex]
distance is given by
[tex]\begin{gathered} \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \sqrt{(6-3)^2+(-3-5)^2} \\ \sqrt{3^2+(-8)^2} \\ \sqrt{9+64} \\ \sqrt{73} \end{gathered}[/tex]
b) Conjugate of z2
as we have ,
[tex]z_2=6-3i[/tex]
so , conjugate is given by
[tex]z_2=6+3i[/tex]
c) we have ,
[tex]\begin{gathered} z_1=3+5i \\ z_2=6-3i \end{gathered}[/tex]
so ,
[tex]\begin{gathered} z_2-z_1=(6-3i)-(3+5i) \\ z_2-z_1=6-3i-3-5i \\ z_2-z_1=3-8i \end{gathered}[/tex]
Final Answer
Hence , the required answers are
a) distance =
[tex]\sqrt{73}[/tex]
b) conjugate = 6 + 3i
c) 3 - 8i
