# Distance and midpoint of complex numbers

##### Examples

###### Lessons

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

###### Free to Join!

StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.

#### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.#### Make Use of Our Learning Aids

#### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.#### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Notes

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.

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

###### Basic Concepts

###### Related Concepts

2

videos

remaining today

remaining today

5

practice questions

remaining today

remaining today