Answer: The required distance between the given points is 13 units.
Step-by-step explanation: We are given to find the distance between the following points :
[tex](4+3i)~~~\textup{and}~~~(9-9i).[/tex]
We know that
the distance between two points z = a + bi and z' = c + di is given by
[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
For the given points, we have
z = 4 + 3i and z' = 9 - 9i.
Therefore, the distance between the points is given by
[tex]D=\sqrt{(9-4)^2+(-9-3)^2}=\sqrt{5^2+(-12)^2}=\sqrt{24+144}=\sqrt{169}=13.[/tex]
Thus, the required distance between the given points is 13 units.
