How to Find the Argument of Complex Numbers

A short tutorial on finding the argument of complex numbers, using an argand diagram to explain the meaning of an argument.
Keep updated with all examination walk throughs and tutorials via mathormaths and mathmathsmathematics

[@bentaylor25]

"What's the argument of a complex number? It's the angle that it makes with the positive real axis"... Already done a better job of explaining that than my teacher. Thank you!

[@Buike_strong]

Not just the positive real axis....
The argument if a complex number is the angle made with the real axis being +ve x or -ve x

[@Burgarfury]

I'm in my 4th year of engineering. I'm ashamed to say this helped me a lot. Nice explanation mate.

[@mohaimen5964]

+Sharukh Mastan bro im 3rd year even im ashamed too. i had a lot of confusion of this angles on 2nd and 3rd quadrant. now i understand it all

[@thatboyjordancool]

You should be ashamed

[@Emmelifall]

+Sharukh Mastan im in second year and yepp feel you!

[@RahulChauhan-tm6ke]

+Sharukh Mastan its been 2 years since i completed my engineering and finally i understood argument of complex number.... lol.... but i m not ashamed, i m happy that i no longer make mistakes while solving it.

[@cuteDselena19]

I'm in the 12th and I don't even plan on doing engineering lols

[@TheResonating]

this deserved a like, my teacher and book did not explain this

[@IsaacTangMusic]

Very True

[@Ray-ye8gz]

You also gave us other important examples which are very critical to the understanding of finding an argument. I appericiate what you did, thanks a lot!!!! :-)

[@harshitdoshi5590]

nice work i am going for classes but could understand this only because of you .

[@m.hazimmadani9948]

Thank you so muchhh!!! Never understood what my teacher taught and I've always hated complex numbers. Im sitting for my a levels tomorrow and this video helped a LOT

[@leechxn4118]

thank you, your explanations are very clear 👍🏻

[@lindsaydunn12]

I watched about 50 videos before this (in a week). Thank you, hoping to give you the credit for this 7 mark Q I am currently working on (which demands the mod, arg, prin arg, and polar form or a quotient of 2 complex numbers). Thank YOU!!

[@mrnoisykry6158]

thank you very much u save me like 2 hrs lookin 4 textbook 5 hr understanding it...

[@lnzpyr]

"You can now find the arguments of z, without discussion and without argument" Nice pun aha. Great video though!

[@xIDOBBYIx]

best video on this i could find! Really simple, thanks.

[@bimaldebnath9075]

I'm glad that you upload this clip........
Thank you so much...

[@NikitaKaminskyy]

The very first example is exactly what I was looking for, thanks!

[@adammalik786]

This is really amazing, thank you :)

[@simransingh8042]

Clearly explained! Thanks!

[@adnanshahriar4435]

Question. In the root 3- i example, you kept the negative sign and didn't subtract it with 2 pi to get the positive angle. But in the last example, you did. Why is that?

[@sketchynote]

+ MathMathsMathematics
For the example at 4:55, I am confused as to why you do not use arctan(3/-3). Isn't the real component in the negative direction? Or are you only paying attention to the absolute value of the distance of each leg of the triangle?

[@mspreddi1]

He keeps on saying you have to be careful. There isn't anything to worry here. I do not get the point why in tan(y/x), the actual values are not substituted and instead only positive values are. For example, in one of the problems here, theta = tan^(-1)(-3/3) then it is theta =-45degrees OR pi/4. Tan is negative in second quadrant. So, in anticlockwise direction, we have to add pi/2 to pi/4 OR pi - pi/4 = 3pi/4.

[@ars9539]

What an immaculate content! Cheers mate with this bo'le of wa'er!

[@mdrafiqulislam8233]

This is really helpful and easy to understand...👍

[@cosmickitty9533]

Amazing thanks. Its hard to find good complex analysis videos.

[@khanthmuu6364]

Nice explanation .Really helpful for me.

[@shivakrishnadasi705]

very nice thank you. For completeness give one example which fall under 3rd quadarant

[@Arnob127]

thanks mannnnn!!!! It helped me a lot!!!!

[@mkdutta9428]

Amazing explanation, Thanks

[@biruksisay7547]

thank you so much for explaining what my teacher couldnt in an hour with a 6 minute video

[@mariaaparicio4276]

Thank you soo much, the only video that helped!

[@brunogrifo4602]

Thx, you spare me like 3 ou 4 hours of research xD

[@tylerkerswell1879]

so what would be the argument for the θ=-π/4 ?

[@encoreartz1028]

Great explanation!

[@Observeryou]

That is really great thank dude !

[@janea710z]

thanks, this helped SO much

[@shcje]

nice explanation it was very helpful

[@efiangeli9893]

thanks! very helpful!

[@MrUtkarsh7723]

you made it clear . thank you

[@chandanadalai1656]

loved it sir... ♥

[@NotSkynut]

You’re an absolute legend

[@songohan393]

Imagine studying without such great videos

[@rachergaming4338]

Thanku sir this is truly understanding 😘😘

[@manpreetsingh9772]

how to find argument if two number is in ratio?

[@leopard_editz1099]

Thanks man wonderful

[@d0oz3yduck48]

how do you but the answer in the form of r

[@asmcriminaL]

thanks a lot, really helped.

[@michellehui6270]

Thank you!

[@kevincharles9864]

yo my nigguh this video was so helpful thank you my nigguh bless up

[@mukeshpant8669]

Great job

[@christopherb6879]

tysm u helped so much

[@awelti63]

thank you wholeheartedly, my 'elite university' tries to filter out students by explaining material badly (objectively speaking) and demanding that stundent then should understand and be able to use the theorie. But one can also explain it well and understandable

[@aashalkamdar9576]

So helpful!!

[@balammac4366]

thank u Sir it helped me

[@rasinshuriken]

y didn't he used tan-inverse of ( "-ive 3/3 ) at 4:45?

[@geoinformaticszone]

Helped me alot. I couldnt understand in class

[@Cosmic._Vibes]

Thank you very much :D

[@user-lj4hl4xg3w]

Thank you so much

[@liltv2012]

Thank you!!!

[@manofpowers25]

Thanks a lot

[@subhandin3435]

no log examples?

[@danny10846]

Derren Brown???

[@shribala1853]

very helpful video

[@haroldcliffton4197]

Thanks a lot.

[@akhif9504]

Thanks a bunch

[@meryemciftci2554]

okay, I got that in most of the cases we are taking the angle in between 0 an 2pi. What if I want to take the angle in between -pi and pi? What should I take into consideration? Thanks for the video btw

[@mikael132]

that is exactly what is the general rule.
always write argument in -pi to pi

[@jipeh]

Thank you.

[@nertilaismailaj3734]

extremely helpful, last year of high school, advanced mathematics

[@ronaldoheta7825]

hahaha o nertile sapo te gjeta n nje koment n youtube (ronaldo)

[@nertilaismailaj3734]

hiii

[@ronaldoheta7825]

+Nertila Ismailaj na ka zen halli :p

[@user-lk7pt4ze4z]

thank you so much

[@kayagunduz7490]

thank you !

[@spuefire9862]

Thank you

[@ankuxtha8788]

thank you ☺

[@ronaldomapp7718]

Thx alot..u sir.....is a monsta

[@AnandKumar-gp6qh]

Thank you ..

[@quin802]

What is an argument of 5i?

[@anthonypascual9347]

Thanks!

[@thinkvasanth]

thanks! it helped :)

[@Kevin-ju7wb]

on example 3 i tried it and got 45 not 3/4pi... how did that happen?

[@ibraheem1224]

Your answer must have come in degrees and not in radians, make sure to check!

[@franciskatende1566]

God bless you for this!

[@rajithasampath8033]

Thanks bro

[@cdperson8271]

Dear,I want to ask when a given argument how to find z.
Ex. arg(z)=π/4 ,z is not equal to zero.
1.imag(z²)=Re(z²)
2.Imag(z²)=0
3. Re(z²)=0

[@tayyabashabbir5327]

thanku sir 😍

[@doyoarero5599]

Thanks

[@InfamousBananaGoblin]

at 2:07 he pulls pi/3 out of nowhere and forgets to explain it can someone help me?

[@vince7079]

generally the angle theta is arctan(y/x)

[@nakulsada6410]

find argument of 1+i/1-root3 please solve

[@supbrosup100]

sooooo much better than university lecturers

[@BHxSnoip]

Sad but very true. Great video

[@dwyanemartin9232]

THANKSS.......

[@courtneyolsen7483]

for the second example, why can't it just be 11pi/6 instead of -pi/6??????

[@abbatiali6315]

you ultimately help me sir

[@RomanBilliard]

thank you

[@shwetashajil3983]

Thank you sooooo much...helped alotttt! :D

[@jayamkodi7476]

Hi

[@jayamkodi7476]

Pls comment pls

[@shwetashajil3983]

hi

[@jayamkodi7476]

Hi

[@DeepakLaxkar147]

for arg(-3+3i) the value of theta should be -pi/4 (that is -45) but you have done it without considering sign of real part.

[@marq6325]

Yep agreed

[@blizzaroxxx]

4:46 why is it 3/3 and not 3/-3?

[@shereencher_ree_n103]

Thinking that maybe it's only shown in the arg(z) part? I'm pretty confused too sorry

[@blizzaroxxx]

@@shereencher_ree_n103 apparently only absolutely value goes into there if it's arctan

[@sonalideshpande158]

Because we have already considered the -ve sign by placing it in the 2nd quadrant

[@minatismathematics641]

Length can't be negative. So we have to take positive number

[@vince7079]

liked the part at 3:34 , i was having big problems recalling this.

[@sidharthr6615]

thanks

[@nibz89]

The arc tan of root 3 = pi/3 , in radians that is equivalent to 60 degrees, and the tan inverse of root 3 is 60 indeed, you need a calculator for that part

[@shahino123]

THANKSSS

[@puffponken4711]

Legend

[@nurul7018]

what arg(3)?? and arg(2)

[@DrunkyDude97]

Nurul Nurfatiah
following the same method it would be 0 as these complex numbers don't have an imaginary value to begin with

[@clhe3375]

wait..the last question was x=-3 and y is 3, so how come its tan(3/3) and not tan(3/-3)???

[@duckymomo7935]

Celina Lim
Because this isn't polar form

[@skolix909]

We are looking at the absolute values. You cannot get a negative length of a triangle.

[@himashreedas8401]

in modulus, -3 becomes 3

[@JesusChild4848]

i love that british accent :D

[@Echyy]

Tysmm

[@mikael132]

guys always report the argument in the interval -π to π

[@lishakumar2419]

Am I the only one who loves his accent 🥺🥺❤️