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.
Basic concepts: Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2),
Related concepts: Imaginary zeros of polynomials,

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=(real2−real1)2+(im2−im1)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‾=(5−2i)\overline{z}=(5-2i)
    a)
    find the distance between the two complex numbers

    b)
    find the midpoint between the two complex numbers

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8.
Imaginary and Complex Numbers
8.1
Introduction to imaginary numbers
8.2
Complex numbers and complex planes
8.3
Adding and subtracting complex numbers
8.4
Complex conjugates
8.5
Multiplying and dividing complex numbers
8.6
Distance and midpoint of complex numbers
8.7
Angle and absolute value of complex numbers
8.8
Polar form of complex numbers
8.9
Operations on complex numbers in polar form
Trigonometry
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