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- Imaginary and Complex Numbers

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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: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$

Related Concepts: Imaginary zeros of polynomials

Notes:

midpoint formula $midpoint=\frac{real_2+real_1}{2}+\frac{im_2+im_1}{2}i$

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

midpoint formula $midpoint=\frac{real_2+real_1}{2}+\frac{im_2+im_1}{2}i$

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

- 1.Given the two complex numbers: $z=(3+i) ; w=(1+3i)$a)find the distance between the two complex numbersb)find the midpoint between the two complex numbers
- 2.Given the complex number: $z=(5+2i)$, and its conjugate $\overline{z}=(5-2i)$a)find the distance between the two complex numbersb)find the midpoint between the two complex numbers

19.

Imaginary and Complex Numbers

19.1

Introduction to imaginary numbers

19.2

Complex numbers and complex planes

19.3

Adding and subtracting complex numbers

19.4

Complex conjugates

19.5

Multiplying and dividing complex numbers

19.6

Distance and midpoint of complex numbers

19.7

Angle and absolute value of complex numbers

19.8

Polar form of complex numbers

19.9

Operations on complex numbers in polar form

We have over 860 practice questions in Sixth Year Maths for you to master.

Get Started Now19.1

Introduction to imaginary numbers

19.2

Complex numbers and complex planes

19.3

Adding and subtracting complex numbers

19.4

Complex conjugates

19.5

Multiplying and dividing complex numbers

19.6

Distance and midpoint of complex numbers

19.7

Angle and absolute value of complex numbers

19.8

Polar form of complex numbers

19.9

Operations on complex numbers in polar form