Still Confused?

Try reviewing these fundamentals first.

- Home
- AU Year 12 Maths
- Imaginary and Complex Numbers

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that last lesson.

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Lesson: 1a8:52
- Lesson: 1b5:58
- Lesson: 2a2:57
- Lesson: 2b2:26

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

22.

Imaginary and Complex Numbers

22.1

Introduction to imaginary numbers

22.2

Complex numbers and complex planes

22.3

Adding and subtracting complex numbers

22.4

Complex conjugates

22.5

Multiplying and dividing complex numbers

22.6

Distance and midpoint of complex numbers

22.7

Angle and absolute value of complex numbers

22.8

Polar form of complex numbers

22.9

Operations on complex numbers in polar form

We have over 1040 practice questions in AU Year 12 Maths for you to master.

Get Started Now22.1

Introduction to imaginary numbers

22.2

Complex numbers and complex planes

22.3

Adding and subtracting complex numbers

22.4

Complex conjugates

22.5

Multiplying and dividing complex numbers

22.6

Distance and midpoint of complex numbers

22.7

Angle and absolute value of complex numbers

22.8

Polar form of complex numbers

22.9

Operations on complex numbers in polar form