Distance and midpoint of complex numbers

Distance and midpoint of complex numbers

We know how to find the distance and the midpoint between two points on a Cartesian plane, but what if we are dealing with a complex plane? It turns out that the formulas that are used to find the distance and the midpoint between two complex numbers are very similar to the formulas we use for the Cartesian points. In this section, we will learn how to use the midpoint formula and the distance formula for Complex numbers.

Lessons

Notes:

midpoint formula
midpoint=real2+real12+im2+im12imidpoint=\frac{real_2+real_1}{2}+\frac{im_2+im_1}{2}i

distance formula
d=(real2real1)2+(im2im1)2d=\sqrt{(real_2-real_1)^2+(im_2-im_1)^2}

  • 1.
    Given the two complex numbers: z=(3+i);w=(1+3i) z=(3+i) ; w=(1+3i)
    a)
    find the distance between the two complex numbers

    b)
    find the midpoint between the two complex numbers


  • 2.
    Given the complex number: z=(5+2i) z=(5+2i), and its conjugate z=(52i)\overline{z}=(5-2i)
    a)
    find the distance between the two complex numbers

    b)
    find the midpoint between the two complex numbers