From Förberedande kurs i matematik 2

Revision as of 12:04, 7 April 2008 (edit) Oskar (Talk | contribs) (Ny sida: {{NAVCONTENT_START}} <center> Bild:3_2_1d-1(2).gif </center> {{NAVCONTENT_STOP}} {{NAVCONTENT_START}} <center> Bild:3_2_1d-2(2).gif </center> {{NAVCONTENT_STOP}}) ← Previous diff		Current revision (09:31, 29 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	If we calculate the expression, we get the answer at once,
-	<center> [[Bild:3_2_1d-1(2).gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>\begin{align}
-	{{NAVCONTENT_START}}	+	z-\bar{w}+u
-	<center> [[Bild:3_2_1d-2(2).gif]] </center>	+	&= (2+i)-(2-3i)+(-1-2i)\\[5pt]
-	{{NAVCONTENT_STOP}}	+	&= 2-2-1+(1+3-2)i\\[5pt]
		+	&= -1+2i\,\textrm{.}
		+	\end{align}</math>}}
		+
		+	If, on the other hand, we interpret the expression in terms of vectors, we must first understand the vector <math>\bar{w}</math> geometrically. When we take the complex conjugate of <math>w</math>, we change the sign of the imaginary part, which is the same as reflecting <math>w</math> in the real axis.
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		+	[[Image:3_2_1_d1.gif|center]]
		+
		+	We can then construct the expression <math>z-\bar{w}+u</math> one term at a time.
		+
		+	[[Image:3_2_1d-2(2).gif|center]]

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Current revision

If we calculate the expression, we get the answer at once,

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

If, on the other hand, we interpret the expression in terms of vectors, we must first understand the vector \displaystyle \bar{w} geometrically. When we take the complex conjugate of \displaystyle w, we change the sign of the imaginary part, which is the same as reflecting \displaystyle w in the real axis.

We can then construct the expression \displaystyle z-\bar{w}+u one term at a time.