Units Digit?

[PreranaMohanty]

Extremely helpful. Continue making such beautiful and knowledgable contents.😊

[Crimsonraziel]

My prof wouldn't give full points until I first proof this pattern continues indefinitely or at least until 3^126. "You don't get full credit for guessing the right answer."

[ufogrindizer]

It's even easier if you change the base to 9.

3^126 = 9^63
Here the pattern are 9 if the exponent is odd and 1 if it's even.
9^1 = 9
9^2 = 81
9^3 = 729
Etc.

Since 63 is odd then the unit number is 9.

[vidlover]

Oh this is sort of like the arithmetic sequence with i the imaginary number. i^1=sqrt{-1} i^2=-1 ; i^3=-i and i^4=1 and so on and so forth for i^5 ; i^6 ; i^7 and i^8 you just look for the multiple of 4 of the power and add 1 2 or 3 to it to see what it is. Since 124 is the nearest power of 4 to 126, then you add 2 to get to 126, therefore it will have a units digit of 9. Since any power that's 2, 6, 10, 14, 18, etc. will have a units digit of 9.

[agiomancer]

If anyone is interested, this was taught to us in Number Theory. Though I'm not sure if it's exclusive to that subject or just something our professor personally chose to teach us.

[billanderson]

I understand "units" better as ones.

[rdtyphon]

Thank you for what you do, these videos are very informative and useful, i hope you have a nice life, it's especially hard to find people passionate about maths in my country this is a great chanmel for people like me

[sreedharperupally]

Superb 👌🏼👌🏼👌🏼👌🏼👌🏼
Thank You Sir 🙏🏼🙏🏼🙏🏼🙏🏼

[TheFman]

Thank you. This is such a useful skill to have. I wish I had this skill during my last job interview.

[anildeshkar]

Excellent development. I was working the same way but could not formulate

[daveb]

I love your videos.. I always learn something new!

[opufy]

This reminds me of calculus when we did xth derivative of sinx

[RelaxedPuppy]

I love the way you teach. So clear and concise.

[saiphaneeshk.h.]

What if the remider is 0?
Is it the last one?

[jp-wdqy]

That’s great. Where would this sum come in useful?

[sushant]

Can you make vedios on linear algebra and vector space there is no simple vedios for that .

[Bobsmith-yfoy]

Brilliant. But why would anyone ever want to know that?

[UtkarshTiwari-wp]

what if the remainder is 0 or 1, would it mean that the required digit will be the 1st number?

[dougr.]

Almost a complete explanation. One important step is sketched out only….. listeners must figure out why

[patriciaceli]

Gracias profesor!!! Gracias por ayudarnos a aprender! ❤