From Förberedande kurs i matematik 2

Revision as of 12:02, 7 April 2008 (edit) Oskar (Talk | contribs) (Ny sida: {{NAVCONTENT_START}} <center> Bild:3_2_1b-1(2).gif </center> {{NAVCONTENT_STOP}} {{NAVCONTENT_START}} <center> Bild:3_2_1b-2(2).gif </center> {{NAVCONTENT_STOP}}) ← Previous diff		Current revision (09:21, 29 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	We can easily calculate <math>z+u</math> and <math>z-u</math>,
-	<center> [[Bild:3_2_1b-1(2).gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\begin{align}
-	{{NAVCONTENT_START}}	+	z+u &= 2+i+(-1-2i) = 2-1+(1-2)i = 1-i,\\[5pt]
-	<center> [[Bild:3_2_1b-2(2).gif]] </center>	+	z-u &= 2+i-(-1-2i) = 2+1+(1+2)i = 3+3i,
-	{{NAVCONTENT_STOP}}	+	\end{align}</math>}}
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		+	and then mark them on the complex plane.
		+
		+	An alternative is to view <math>z</math> and <math>u</math> as vectors and <math>z+u</math> as a vector addition of <math>z</math> and <math>u</math>.
		+
		+	[[Image:3_2_1_b1.gif|center]]
		+
		+	We can either view the vector subtraction <math>z-u</math> as <math>z+(-u)</math>,
		+
		+	[[Image:3_2_1_b2.gif|center]]
		+
		+	or interpret <math>z-u</math> from the vector relation
		+
		+	{{Displayed math||<math>z=(z-u)+u\,,</math>}}
		+
		+	i.e. <math>z-u</math> is the vector we add to <math>u</math> to arrive at <math>z</math>.
		+
		+	[[Image:3_2_1_b3.gif|center]]

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Current revision

We can easily calculate \displaystyle z+u and \displaystyle z-u,

\displaystyle \begin{align} z+u &= 2+i+(-1-2i) = 2-1+(1-2)i = 1-i,\\[5pt] z-u &= 2+i-(-1-2i) = 2+1+(1+2)i = 3+3i, \end{align}

and then mark them on the complex plane.

An alternative is to view \displaystyle z and \displaystyle u as vectors and \displaystyle z+u as a vector addition of \displaystyle z and \displaystyle u.

We can either view the vector subtraction \displaystyle z-u as \displaystyle z+(-u),

or interpret \displaystyle z-u from the vector relation

\displaystyle z=(z-u)+u\,,

i.e. \displaystyle z-u is the vector we add to \displaystyle u to arrive at \displaystyle z.