What is the distance between the
numbers negative three 𝑖 and seven 𝑖 in the complex plane?
Let’s draw an Argand diagram to
help us and mark negative three 𝑖 and seven 𝑖. Both numbers are purely imaginary
and so lie on the imaginary axis of the complex plane. And so the distance between them is
measured along this axis. To get from negative three 𝑖 to
zero, you have to move three units up. And continuing from zero to seven
𝑖, you have to move a further seven units. So the total distance is three plus
seven, which is 10.