From Förberedande kurs i matematik 2

Revision as of 12:09, 7 April 2008 (edit) Oskar (Talk | contribs) (Ny sida: {{NAVCONTENT_START}} <center> Bild:3_2_3-1(2).gif </center> {{NAVCONTENT_STOP}} {{NAVCONTENT_START}} <center> Bild:3_2_3-2(2).gif </center> {{NAVCONTENT_STOP}}) ← Previous diff		Current revision (09:51, 29 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	If we mark the three complex numbers in the plane, we see that the fourth corner will have <math>3+2i</math> and <math>3i</math> as neighbouring corners.
-	<center> [[Bild:3_2_3-1(2).gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	[[Image:3_2_3_1.gif|center]]
-	{{NAVCONTENT_START}}	+
-	<center> [[Bild:3_2_3-2(2).gif]] </center>	+	In order to find the fourth corner, we use the fact that in a square opposite sides are parallel and all sides have the same length. This means that the vector from <math>1+i</math> to <math>3i</math> is equal to the vector from <math>3+2i</math> to the fourth corner.
-	{{NAVCONTENT_STOP}}	+
		+	[[Image:3_2_3_2.gif|center]]
		+
		+	If we interpret the complex numbers as vectors, this means that the vector from
		+	<math>1+i</math> to <math>\text{3}i</math> is
		+
		+	{{Displayed math||<math>3i-(1+i) = -1+2i</math>}}
		+
		+	and we obtain the fourth corner if we add this vector to the corner <math>3+2i</math>,
		+
		+	{{Displayed math||<math>3+2i+(-1+2i) = 2+4i\,\textrm{.}</math>}}

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Current revision

If we mark the three complex numbers in the plane, we see that the fourth corner will have \displaystyle 3+2i and \displaystyle 3i as neighbouring corners.

In order to find the fourth corner, we use the fact that in a square opposite sides are parallel and all sides have the same length. This means that the vector from \displaystyle 1+i to \displaystyle 3i is equal to the vector from \displaystyle 3+2i to the fourth corner.

If we interpret the complex numbers as vectors, this means that the vector from \displaystyle 1+i to \displaystyle \text{3}i is

\displaystyle 3i-(1+i) = -1+2i

and we obtain the fourth corner if we add this vector to the corner \displaystyle 3+2i,

\displaystyle 3+2i+(-1+2i) = 2+4i\,\textrm{.}