COMPLEX NUMBERS | How to Add, Subtract, Multiply and Divide Complex Numbers

Let's go over Complex Numbers!
Learn how to add complex numbers by combining like terms, subtract complex numbers by subtracting like terms, multiply complex numbers using the FOIL method, and divide complex numbers using complex conjugates.
Comment what other topics you'd like the A+ Tutor to review! New videos are uploaded every week.
Watch Next:
How to Add and Subtract Complex Numbers: • How to Add and Subtrac...
How to Multiply Complex Numbers: • How to Multiply Comple...
How to Divide Complex Numbers: • How to Divide Complex ...
Timeline:
00:00 Intro
00:11 Definition of Complex Numbers
02:19 Adding Complex Numbers
04:48 Subtracting Complex Numbers
07:42 Multiplying Complex Numbers
10:29 Dividing Complex Numbers
14:44 Ending
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[@TheAPlusTutor]

For the second example in Dividing Complex Numbers, the negative sign was cut off. The correct answer is -52 + 14i / 25.

[@MoonGirl-my4zn]

Thanks

[@megatrondeathray6574]

I was so confused lol. Thanks for the clarification.

[@johnkennedycamins5507]

@@MoonGirl-my4zn >

[@6vll]

the first example of division how u got 8i???

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[@TheAPlusTutor]

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[@TheAPlusTutor]

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[@TheAPlusTutor]

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[@TheAPlusTutor]

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[@TheAPlusTutor]

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[@LuhuhuGahhw]

On subtracting, example no.1 it should be -3-8i ? Or I am mistaken?

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[@TheAPlusTutor]

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[@TheAPlusTutor]

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[@JhusThin]

Easy and simple to understand 😅

[@divineobot1605]

You forgot the minus sign on 52, but thank you very much, your video is very helpful.

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[@TheAPlusTutor]

You’re very welcome! I’m glad you enjoyed!

[@pelasgeuspelasgeus4634]

Excuse me, why does CN are treated as vectors? Are they numbers or vectors?

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Glad you liked it!

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Thank you so so so much, today in class I kept dozing off (since it's my first hour), and idk why since i went to bed early last night, so I had no clue how to do this, I asked my teacher if I could go to her after at the end of the school day but she had a meeting, and Savvas Realize's (our textbook brand) online website wasn't working so i had no idea where i was going to watch the videos, but I found this video instead, thank you so so much!

[@TheAPlusTutor]

I’m so glad you found this video and it was helpful!! Thanks for your message ❣️ if there’s anything else you’d like me to review just let me know and I can try to make it happen!

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Clear

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[@TheAPlusTutor]

Thank you!

[@latoyaetienne1726]

I have a question, I did the second example three times and I keep getting the result -52+14i/25. After I multiplied the 12i squared to (-1) I got -12...... -40 +14i -12 over 16 + 9 = -52 + 14i / 25........ What am I doing wrong?????

[@TheAPlusTutor]

Thank you so much for your question! You are absolutely right, my negative got cut off in the video, adding a note in the description now!! Thank you!

[@Dereck27]

Your explanation was very good. I understood everything but one thing and that’s the subtraction. Would you group like terms together and then add them? Kinda confused on that

[@TheAPlusTutor]

Thanks for your question! When you subtract, first you want to distribute the minus sign, so basically change all of your signs starting at the minus sign. Then add your like terms. I have another video with more examples of subtraction, so feel free to check that out and let me know if you have any more questions! Or want some more information on subtraction!
ua-cam.com/video/MIxmOXidx4U/v-deo.html

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[@neisesmart6853]

Do you think you can do a video on completing the square? Your videos are really helpful by the way!

[@TheAPlusTutor]

Thank you so much and thank you for the suggestion! Yes, I will be posting a video on that, stay tuned! 😊

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[@TheAPlusTutor]

Thank you for your kind words!! I wish you the best of luck in your journey

[@rsxryzen8629]

Hey excuse me.
Example one of dividing complex numbers.
(8-5i)(8+5i) denominator*
8 multiply by 8 is 64
Shouldn't it be - 5 × 5?

[@TheAPlusTutor]

Hello! Thanks for your question!
Yes! But then you will have i^2 * 25 which is negative 1 so the denominator will become 64 + 25
I hope this helps!

[@jillboone8657]

You taught me better than my math teacher

[@TheAPlusTutor]

I'm glad I could help!

[@evzlen]

7:35 i don't understand how (-6i√2-6i√2) is 12i√2 why is it still √2

[@mcfright_xd3504]

thank you, heheh

[@shadowdulpireal1040]

Can i ask a question
My question is where did the plus come??

[@mexyztv3256]

Little bit confused in the last part dividing complex numbers How did u get -94 +8i

[@TheAPlusTutor]

Thanks for your question!
When you FOIL, you are left with 30i^2 which becomes -30 since i^2 = -1. Then your like terms are -64 and -30 so combining those gives you -94. Then you combine -40i and 48i to get positive 8i.
Hope this clears it up.

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[@vijayush143love4]

Additive inverse of complex numbers video petandi

[@johnlaurencegumapac9447]

In the subtracting complex numbers, this should be the answer:
1. -3-8i
2. 1-12square root of 2i
There should be no positive sign on the middle.

[@johnlaurencegumapac9447]

When using calcu you can use mode 2: complex. You can type the whole equation and you will got that answer

[@nyakallomoshoeu4644]

Hello,isn't negative 52 there?

[@TheAPlusTutor]

Hi, Yes! The negative sign got cut off but yes it is -52 at the end!

[@ogeidnomar4601]

In your addition example where you had 2+3 sq root of 9...
Why did you put 3 instead of 2 in front of sq root of 9???
That small bit is confusing me.

[@ogeidnomar4601]

Nevermind, I completely misunderstood, but figured it out. I forgot Sq roots do not need a 2 as that is the default value (oops on my part :-)))

[@TheAPlusTutor]

Glad you figured it out!! Let me know if you have any other questions I’m always happy to help!!

[@user-bg3jj1dz1v]

on the division part you said we change the sign of the complex numbers but our teacher told us to change the sign of the imaginary part not the whole complex

[@beronicaleih6254]

Hi. Part po ba ang topic na ito sa Abstract Algebra po?😊 Thanks po sa pagsagot.