Question

Find the distance d between z1 = (2 + 2i) and Z2 = (6 – 4i).Express your answer in exact terms and simplify, if needed.d

Answer 1

We can calculate the distance between these two complex numbers z1 = (2+2i) and z2 = (6-4i) as:

$\begin{gathered} d=|z_1-z_2| \\ d=|(2+2i)-(6-4i)| \\ d=|(2-6)+(2-(-4))i| \\ d=|-4+6i| \\ d=\sqrt[]{(-4)^2+(6)^2} \\ d=\sqrt[]{16+36} \\ d=\sqrt[]{52} \\ d=\sqrt[]{4\cdot13} \\ d=2\sqrt[]{13} \end{gathered}$

Answer: the distance is d = 2√13