Math Is Fun Forum

Mystogan

Member

Registered: 2015-08-12

Posts: 12

Complex Numbers

Find the value:

I can do it by substituting each individual term with i,-i,-1 or 1. But is there a way to generalize this type of question, like make a formula for solving it easily?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Complex Numbers

There is a standard move to begin with borrowed from numerical work.

Your expression can be reduced to.

Now you only need to know what i^2 is. The computation is trivial.

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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.

Mystogan

Member

Registered: 2015-08-12

Posts: 12

Re: Complex Numbers

How did you arrive at that expression?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Complex Numbers

The technique is called Hornerization and it is very common in numerical work. I can show you with examples...But it was only a first try perhaps there is something even better...

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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: 10,621

Re: Complex Numbers

hi Mystogan

That series is a geometric progression so you can use the formula:

http://www.mathsisfun.com/algebra/seque … etric.html

Bob

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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

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: Complex Numbers

As bob bundy points out, your series is geometric, and there is a simple formula for the sum of a geometric series. However, as an infinite series, it will not converge.

Mystogan

Member

Registered: 2015-08-12

Posts: 12

Re: Complex Numbers

I see. Thanks for the help.