       Re: How to define the coefficients of a polynomial to

• To: mathgroup at smc.vnet.net
• Subject: [mg100952] Re: [mg100925] How to define the coefficients of a polynomial to
• From: Carl Woll <carlw at wolfram.com>
• Date: Thu, 18 Jun 2009 20:46:00 -0400 (EDT)
• References: <200906180854.EAA20049@smc.vnet.net>

```BHUPALA wrote:
> I have a 10th order polynomial (a0+a1 z+a2 z^2 + ... + an z^10). I
> want to define all the coefficients to be real. I want to substitute z
> = 1+i and extract only real part of it.
>
> I have done this by defining
>
> Element[a0,Reals];
> Element[a1,Reals];
>
>
ComplexExpand is the tool you need:

In:= ComplexExpand[
Re[a0 + a1 z + a2 z^2 + a3 z^3 + a4 z^4 + a5 z^5 + a6 z^6 + a7 z^7 +
a8 z^8 + a9 z^9 + a10 z^10 /. z -> 1 + I]]

Out= a0 + a1 - 2 a3 - 4 a4 - 4 a5 + 8 a7 + 16 a8 + 16 a9

Carl Woll
Wolfram Research

```

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