Question

Find the distance between -2 and 2+2i

Answer 1

`z=a+bi\\\\|z|=√(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|=√((-4)^2+2^2)\\\\=√(16+4)=√(20)=√(4\cdot5)=\sqrt4\cdot\sqrt5=\boxed{2\sqrt5}`