complex numbers

[khalil]

has any1 seen the binomial method?
ive got the heinemann text book and they have this weird way which involves n's and r's
some1 please explain
solve (3-5i)^5 using the binomial method
thanks

[hard]

looks pretty simple, just use the binomial method then to simplify and all use the i^2= -1 etc. Not too sure though so correct me anyone?

[Mao]

expand it as any polynomial, but remember

[khalil]

yer but it says to use the binomial method

[Damo17]

yer but it says to use the binomial method

Then use it:


           

Now using that:















If your not sure on your answer straight away when doing question like this, just put it in your calculator with (a+bi) set in mode and you will see if it is right.

[Damo17]

Khalil: Doesn't the book show the binomial method (like below) and an example?

Binomial Theorem:

           

[khalil]

Khalil: Doesn't the book show the binomial method (like below) and an example?

Binomial Theorem:


yer it does but it contains weird things like n over 0

thanks by the way
           

[khalil]

Can someone do this:
State the values of |z| and Arg z when z equals
-3 cos(- π/3)+ 3i sin (- π/3)

the things that look like n's are pie

[ell]

Can someone do this:
State the values of |z| and Arg z when z equals
-3 cos(- π/3)+ 3i sin (- π/3)

the things that look like n's are pie

Let





To find , first determine what quadrant the complex number is in. Picture an Argand diagram - since the real part is negative and the imaginary part is also negative it is in the 3rd quadrant.

(since the angle must be in the third quadrant)

[khalil]

Wow thanks
the method in the book is much more complex

[bigtick]

-3 cos(- π/3)+ 3i sin (- π/3) = -3 cos(π/3)- 3i sin (π/3) = -3cis(n/3) = 3cis(-2n/3)
|z| = 3, Arg(z) = -2n/3

[Damo17]

Khalil: Doesn't the book show the binomial method (like below) and an example?

Binomial Theorem:

yer it does but it contains weird things like n over 0

thanks by the way

Yeah, there are different ways of expressing the binomial methods. The one that I did above is Newton's generalized binomial theorem. Below is the one you most likely have is your book.



what is crucial in understanding this is:


To understand better lets use an example. The question I did above.



At this point, to save alot of unnecessary working out, know that and are both equal to 1.












It is rather simple once you understand:

[humph]

And of course for small numbers it's much easier to remember the coefficients via Pascal's triangle (though this becomes increasingly impractical for larger numbers).

[Mao]

combinatorics are easier to remember like this:



on top, starting with 9, count down 3 numbers, on the bottom, starting with 1, count up 3 numbers



makes life so much easier

[khalil]

Khalil: Doesn't the book show the binomial method (like below) and an example?

Binomial Theorem:

yer it does but it contains weird things like n over 0

thanks by the way

Yeah, there are different ways of expressing the binomial methods. The one that I did above is Newton's generalized binomial theorem. Below is the one you most likely have is your book.



what is crucial in understanding this is:


To understand better lets use an example. The question I did above.



At this point, to save alot of unnecessary working out, know that and are both equal to 1.












It is rather simple once you understand:

thanks for ur help....i havent done factorials in yr 11 so my understanding of them isnt so great
do u have to use the binomial method a lot ?