Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Division of two complex numbers
Date: Tue, 21 Jan 2025 11:37:20 +0100
Organization: A noiseless patient Spider
Lines: 28
Message-ID: <vmntd0$cq2$1@dont-email.me>
References: <zMjaMvWZUkHX6SOb195JTQnVpSA@jntp>
 <l8LT_eq8GhpxVVQxWtwWIRNR90o@jntp> <f3aJzM9fFsoPFMeeAuDqE0UYFYw@jntp>
 <3OCPm1fExu73aCqhbosWeWpssJM@jntp> <HiiX_DciB8TjyK4p5hsbqJx52xs@jntp>
 <pn08rF_5GGMziz3K6TnJrhlBJek@jntp> <vmm8do$3cetq$2@dont-email.me>
 <1f331uj8cjsge$.rox7zzvx5o63$.dlg@40tude.net>
 <hJUop495V-7lOEA98AQwiM7l6-Q@jntp>
 <206lh7vmixbg$.65ym8wmigyp0$.dlg@40tude.net>
 <kPCV5ohM5LdbWSbXZ-3kSzTr3vQ@jntp>
 <qlzmlt088phs$.1rjp06qe5kzib.dlg@40tude.net> <vmmiic$3f4ok$8@dont-email.me>
 <yipt93joitda$.dpphr6r0qbrd$.dlg@40tude.net> <vmmm0d$3gq5g$2@dont-email.me>
 <9bds61cjwkps.4limb46c5wk9$.dlg@40tude.net> <vmmpf0$3i3gl$1@dont-email.me>
 <vmnsqd$3vmh3$1@dont-email.me>
Reply-To: invalid@example.invalid
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Tue, 21 Jan 2025 11:37:21 +0100 (CET)
Injection-Info: dont-email.me; posting-host="167941bcdca3a92f25c5377ee1395966";
	logging-data="13122"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18TVAHwTBKdrNWsdMAS3ptv"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:eVfmjjkxdqwyfzg2tp4o1MUYWd0=
In-Reply-To: <vmnsqd$3vmh3$1@dont-email.me>
Content-Language: de-DE
Bytes: 2189

Am 21.01.2025 um 11:27 schrieb Moebius:

> Außerdem macht "(a, b)^2 = a^2 + 2ab + b^2" nach wie vor keinen Sinn. 

Let's write the complex number (a, b) in the usual form a + ib. Then

     (a + ib)^2 = a^2 + i2ab + (ib)^2

by the binomial formula (!). Hence

     (a + ib)^2 = a^2 + i2ab + (-1)b^2 = (a^2 - b^2) + i2ab .

And hence

     (a, b)^2 = (a^2 - b^2) + i2ab  (!)

or rather

     (a, b)^2 = (a^2 - b^2, 2ab)

would be correct.

( Knapp daneben ist auch vorbei. :-P )

..
..
..