Linear Algebra: Polar and Exponential Forms of a Complex Number

In this video, we continue our discussion of complex numbers. We discuss the rectangular, Polar and exponential forms of a complex number and why they are useful. We also cover MANY examples of application of these different forms of complex numbers.
00:00 - Introduction
00:15 -The rectangular form of a complex number
01:53 - Polar form of a complex number
08:15 - Example 1
12:05 - Example 2
14:12 - Exponential form
16:50 - Example 3
18:16 - Example 4
20:41 - Example 5
29:48 - Example 6
35:21 - Rules for complex exponentials
36:57 - Example 7
46:50 - Example 8

[@mathszindabad4260]

You are the luckiest one. great art of teaching with melody voice

[@MathforThought]

Thank you!

[@rockstarraushan143]

Really your voice and explanition method is heartouching

[@KIIZAAloysiusAkiiki]

You are nice lecturer

[@selimkahraman1097]

Very well explained, thank you for your time.

[@maxwong3903]

Thank you so much for this video!

[@reeteshreet198]

Thank you, it helped me with my assignment a lot!!!

[@Rex9594]

Much appreciated!

[@Lierjw]

Thanks for your effort ♥️

[@benenaidoo2132]

You're the only one I've found that's explained it so well and done examples

[@MathforThought]

Aww thank you!

[@melody2999]

super helpful! learning this for a modern algebra class

[@MathforThought]

Glad it was helpful!

[@akniyetzhanay1508]

I've been searching for the whole youtube for a such video!
Thank you a lot!

[@MathforThought]

You're welcome!

[@user-le3oy9gd2f]

at 18:05 when u got the angle u went clockwise to make the angle -pi/3 with the line, can i also go anticlockwise? or does the angle HAVE to be between pi & -pi

[@gabrielkuchherbalachiek3870]

Very excellent work

[@williamcripfoe6754]

How did you get -11 pi/4 for example 7 wouldnt it be -14pi/4?

[@pablitofontes]

Hey! I like your videos a lot, thanks for sharing! I am currently giving some lessons online, and I am struggling to find a good software to write on. Yours seems to work really good, what program is it?
Thanks!

[@MathforThought]

Thanks! I use Microsoft OneNote :) .

[@brosthatride8586]

Super helpful

[@robyn.m3031]

Thank you so much. This really helped me with my revision 😊😁

[@zahra-pl1sk]

thanks alot

[@NahidsJunk]

What do I do if my angle is in the wrong quadrant? Let say I have -3.49i and -4.257. I got the angle 37.351. This is in the third quadrant. What do I do now?

[@MathforThought]

That just means you need to manually add on 180 degrees since the measure would be the same.

[@MargaretSimiyu]

if i may ask where are getting the pie symbol when cmputing after inverse tan

[@MathforThought]

Which example?

[@rabewarmoradi2247]

For example 4, could the angle also be written as 5pi/3?

[@MathforThought]

No since the terminal arm extends from x to the -y axis so we have to go clockwise.

[@sarahngao1574]

Wow😊

[@akafire793]

bro tHANK YOU

[@sammtanX]

in Example 7, I think there is the mistake for e exponent. Shouldn't it be e^(i*-14pi/4))?

[@MathforThought]

Yes you are right. I will correct these one day!

[@imansaid2321]

What is the meaning of the 𝚿 symbol?

[@MathforThought]

It's the angle you rotate by.

[@ghinaghina7222]

u have smthng wrong at minute 42:32 u said -9.pie.i/6 but u wrote it -9.pie.i/9 and continued with wrong

[@MathforThought]

No it's still right. I did the right calculations but I just wrote the number wrong. I continued the math with the correct answers.
Thank you for that typo though. I will eventually revise these.

[@godfreypigott]

"Euler" is pronounced "Oiler". A mathematician should know that.

[@MathforThought]

Haha yes. My bad.

[@yupko3426]

Karen?

[@godfreypigott]

@@yupko3426 I'm sure that means something to you, but it means nothing to me.