4u complex numbers (1 Viewer)

[jnney]

Express -root3-i in modulus–argument form.

I got 2cis30 - the angle by doing the tan inverse of 1/root3.

Answer says 2cis(-5pi/6)


it's wrong to say 2cis30 isn't it, because the coordinate is in the 3rd quadrant?

can i say 2cis270 instead?

 

[ohexploitable]

by convention the simplest form of the argument is expressed between -pi and pi

 

[Hermes1]

Express -root3-i in modulus–argument form.

I got 2cis30 - the angle by doing the tan inverse of 1/root3.

Answer says 2cis(-5pi/6)


it's wrong to say 2cis30 isn't it, because the coordinate is in the 3rd quadrant?

can i say 2cis270 instead?

theres something called the principle argument which means you angle has to be between 0 and 180, if its not you go the other way round.
-root 3-i is in the 3rd quadrant, so thats why its 7pi/6 which by principal argument regulations has to be written as -5pi/6

gud to see someone getting ahead and starting 4 unit early.

 

[jnney]

theres something called the principle argument which means you angle has to be between 0 and 180, if its not you go the other way round.
-root 3-i is in the 3rd quadrant, so thats why its 7pi/6 which by principal argument regulations has to be written as -5pi/6

gud to see someone getting ahead and starting 4 unit early.

OH THAT'S RIGHT. Forgot about that for a second.


Also, for 'show that (-root3-i)^6 is a real number,

i've replaced the inside brackets with 2cis5pi/6. I dont know what to do next.

 

[ohexploitable]

OH THAT'S RIGHT. Forgot about that for a second.


Also, for 'show that (-root3-i)^6 is a real number,

i've replaced the inside brackets with 2cis5pi/6. I dont know what to do next.

 

[jnney]

what happened to the denominator 6?

 

[Hermes1]

what happened to the denominator 6?

its a formula with cis that when you put it to the power of something the power gets multiplied into the argument.



do u have terry lee 4u? if not get it, he covers everything like this in good detail

 

[jnney]

Yes I have it, I'll look at it right now.

Thanks guys!

 

[Alkanes]

Self learning or tutoring?

 

[jnney]

Both? I just started 4u today so exciting LOL

 

[Alkanes]

Haha nice. Yea i started it too but not this far yet.

 

[jnney]

What topic are you doing?

 

[Alkanes]

This one but just the basics like multiplying/adding i

 

[jnney]

Are you doing terry lee too?

 

[Alkanes]

I don't go to terry lee

 

[jnney]

No the textbook.

 

[Alkanes]

Lol i don't have the textbook atm. Only 4u book i have is cambridge.

 

[khfreakau]

what happened to the denominator 6?

It's called De Moivre's theorem - as arj1 explained, you can simply multiply the power into the angle. However, that's not to say that you can't still expand out (cisx)^n normally by making it cosx + isinx and binomially expanding, which will come in handy in later questions

 

[Shadowdude]

It's called De Moivre's theorem - as arj1 explained, you can simply multiply the power into the angle. However, that's not to say that you can't still expand out (cisx)^n normally by making it cosx + isinx and binomially expanding, which will come in handy in later questions

Ah, I got screamed at - kinda - by my Algebra lecturer for using 'cis'. Never used it again afterwards =P

 

[AAEldar]

Ah, I got screamed at - kinda - by my Algebra lecturer for using 'cis'. Never used it again afterwards =P

Don't you use now though anyway?