Math Is Fun Forum

coolbee

Member

Registered: 2016-04-05

Posts: 19

complex numbers (imaginary 5th root)

hi,

Q. If 

is the imaginary fifth root of 2 and

, then find the value of

.

please help

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: complex numbers (imaginary 5th root)

hi coolbee

I did it like this:

so

and

So now it's just a matter of substituting into the given expression in x.  You'll find there's lots of cancelling.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

coolbee

Member

Registered: 2016-04-05

Posts: 19

Re: complex numbers (imaginary 5th root)

thank you bob

here is one more question:-

If

and

,
then find the value of

(p∈N.)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: complex numbers (imaginary 5th root)

Hi coolbee;

Has the problem  been copied correctly?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

coolbee

Member

Registered: 2016-04-05

Posts: 19

Re: complex numbers (imaginary 5th root)

Yes bobbym.
but what's wrong?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: complex numbers (imaginary 5th root)

Hi;

For one thing it does not converge to a single number.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: complex numbers (imaginary 5th root)

hi coolbee

I think the following might work:

The expression you are asked to evaluate looks like it is the coefficient in the above for the term containing x^{3p}

You can determine this coefficient independently using the binomial expansion.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob