Question

Find the distance between -2 and 2+2i

Answer 1

$z=a+bi\\\\|z|=\sqrt{a^2+b^2}\\\\z_1=-2,\ z_2=2+2i\\\\\text{the distance between}\ z_1\ \text{and}\ z_2:\\\\|z_2-z_1|=|-2+2i-2|=|-4+2i|=\sqrt{(-4)^2+2^2}\\\\=\sqrt{16+4}=\sqrt{20}=\sqrt{4\cdot5}=\sqrt4\cdot\sqrt5=\boxed{2\sqrt5}$