Räkna med komplexa tal - Versionshistorik

Hakan: /* Öva själv */

2016-11-29T15:47:09Z

Öva själv

← Äldre version		Versionen från 29 november 2016 kl. 15.47
Rad 45:		Rad 45:

	{{khanruta \| [https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-complex-numbers/e/multiplying_complex_numbers Multiply complex numbers]}}		{{khanruta \| [https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-complex-numbers/e/multiplying_complex_numbers Multiply complex numbers]}}
	{{khanruta \| [https://www.khanacademy.org/math/algebra-home/alg-complex-numbers/alg-complex-conjugates-and-dividing-complex-numbers/e/dividing_complex_numbers Divide complex numbers}}		{{khanruta \| [https://www.khanacademy.org/math/algebra-home/alg-complex-numbers/alg-complex-conjugates-and-dividing-complex-numbers/e/dividing_complex_numbers Divide complex numbers]}}
	{{khanruta \| [https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-fractions-2/e/complex-fractions Simplify hairy fractions] }}		{{khanruta \| [https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-fractions-2/e/complex-fractions Simplify hairy fractions] }}

2016-11-29T15:46:40Z

Exempel

← Äldre version		Versionen från 29 november 2016 kl. 15.46
Rad 41:		Rad 41:

	{{clear}}		{{clear}}

			=== Öva själv ===

			{{khanruta \| [https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-complex-numbers/e/multiplying_complex_numbers Multiply complex numbers]}}
			{{khanruta \| [https://www.khanacademy.org/math/algebra-home/alg-complex-numbers/alg-complex-conjugates-and-dividing-complex-numbers/e/dividing_complex_numbers Divide complex numbers}}
			{{khanruta \| [https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-fractions-2/e/complex-fractions Simplify hairy fractions] }}

	== Fundera ==		== Fundera ==

2016-03-01T15:34:00Z

← Äldre version		Versionen från 1 mars 2016 kl. 15.34
Rad 1:		Rad 1:
			[[Category:Matematik]] [[Category:Ma4]] [[Category:Aritmetik, algebra och geometri]] [[Category:Komplexa tal]]

	== Potenser av i ==		== Potenser av i ==

2015-04-01T09:34:14Z

Potenser av i

← Äldre version		Versionen från 1 april 2015 kl. 09.34
Rad 13:		Rad 13:
	\| <math>i^4 = i^2 \cdot i^2</math> \|\| <math>-1 \cdot -1 = 1</math>		\| <math>i^4 = i^2 \cdot i^2</math> \|\| <math>-1 \cdot -1 = 1</math>
	\|-		\|-
	\| <math>i^5~~</math> \|\| <math>-~~ \~~: 1</math>~~		\| <math>i^5 = i \cdot i^4</math> \|\| <math>i \cdot 1 = i</math>
	\|-
	~~\| <math>~~i^6</math> \|\| <math>- \: 1</math>
	\|}		\|}

2015-04-01T09:32:54Z

Potenser av i

← Äldre version		Versionen från 1 april 2015 kl. 09.32
Rad 5:		Rad 5:
	! potens av <math>i</math> !! resultat		! potens av <math>i</math> !! resultat
	\|-		\|-
	\| <math>i</math> \|\| i		\| <math>i</math> \|\| <math>i </math>
	\|-		\|-
	\| <math>i^2</math> \|\| <math>- \: 1</math>		\| <math>i^2</math> \|\| <math>- \: 1</math>
	\|-		\|-
	\| <math>i^3 = i \cdot i^2</math> \|\| <math>- \: i</math>		\| <math>i^3 = i \cdot i^2</math> \|\| <math>-1 \cdot i = - \: i</math>
	\|-		\|-
	\| <math>i^4 = i^2 \cdot i^2</math> \|\| <math>-1 \cdot -1 = 1</math>		\| <math>i^4 = i^2 \cdot i^2</math> \|\| <math>-1 \cdot -1 = 1</math>

2015-04-01T09:31:02Z

Potenser av i

← Äldre version		Versionen från 1 april 2015 kl. 09.31
Rad 9:		Rad 9:
	\| <math>i^2</math> \|\| <math>- \: 1</math>		\| <math>i^2</math> \|\| <math>- \: 1</math>
	\|-		\|-
	\| <math>i^3 = i \cdot i^2</math> \|\| <math>- \: 1</math>		\| <math>i^3 = i \cdot i^2</math> \|\| <math>- \: i</math>
	\|-		\|-
	\| <math>i^4</math> \|\| <math>- \: 1</math>		\| <math>i^4 = i^2 \cdot i^2</math> \|\| <math>-1 \cdot -1 = 1</math>
	\|-		\|-
	\| <math>i^5</math> \|\| <math>- \: 1</math>		\| <math>i^5</math> \|\| <math>- \: 1</math>

2015-04-01T09:29:12Z

Exempel

← Äldre version		Versionen från 1 april 2015 kl. 09.29
Rad 37:		Rad 37:
	<br />		<br />

	: <math>=\frac{ 6-7 i - 2}{13} = \frac{ 4-7 i }{13} = \frac{ 4}{13} - \frac{7 i }{13}</math>		: <math>=\frac{ 6-7 i - 2}{13} = \frac{ 4-7 i }{13} = \frac{ 4}{13} - \frac{7 }{13} \: i</math>

	{{clear}}		{{clear}}

2015-04-01T09:28:38Z

Exempel

← Äldre version		Versionen från 1 april 2015 kl. 09.28
Rad 37:		Rad 37:
	<br />		<br />

	: <math>=\frac{ 6-7 i - 2}{13} = \frac{ 4-7 i }{13} = \frac{ 4}{13} + \frac{ -7 i }{13}</math>		: <math>=\frac{ 6-7 i - 2}{13} = \frac{ 4-7 i }{13} = \frac{ 4}{13} - \frac{7 i }{13}</math>

	{{clear}}		{{clear}}

2015-04-01T09:27:57Z

Exempel

← Äldre version		Versionen från 1 april 2015 kl. 09.27
Rad 35:		Rad 35:

	: <math> \frac{(2-i)(3-2 i)}{(3+2 i)(3-2 i)} = \frac{ 6-4 i - 3 i + 2 i^2}{3^2+2^2} = \frac{ 6-7 i + 2 (- 1)}{9+4} = </math>		: <math> \frac{(2-i)(3-2 i)}{(3+2 i)(3-2 i)} = \frac{ 6-4 i - 3 i + 2 i^2}{3^2+2^2} = \frac{ 6-7 i + 2 (- 1)}{9+4} = </math>
			<br />

	: <math>=\frac{ 6-7 i - 2}{13} = \frac{ 4-7 i }{13} = \frac{ 4}{13} + \frac{ -7 i }{13}</math>		: <math>=\frac{ 6-7 i - 2}{13} = \frac{ 4-7 i }{13} = \frac{ 4}{13} + \frac{ -7 i }{13}</math>

2015-04-01T09:27:33Z

Exempel

← Äldre version		Versionen från 1 april 2015 kl. 09.27
Rad 34:		Rad 34:
	då förlänger vi med konjugatet		då förlänger vi med konjugatet

	: <math> \frac{(2-i)(3-2 i)}{(3+2 i)(3-2 i)} = \frac{ 6-4 i - 3 i + 2 i^2}{3^2+2^2} = \frac{ 6-7 i + 2 (- 1)}{9+4} = \frac{ 6-7 i - 2}{13} = \frac{ 4-7 i }{13} = \frac{ 4}{13} + \frac{ -7 i }{13}</math>		: <math> \frac{(2-i)(3-2 i)}{(3+2 i)(3-2 i)} = \frac{ 6-4 i - 3 i + 2 i^2}{3^2+2^2} = \frac{ 6-7 i + 2 (- 1)}{9+4} = </math>

			: <math>=\frac{ 6-7 i - 2}{13} = \frac{ 4-7 i }{13} = \frac{ 4}{13} + \frac{ -7 i }{13}</math>

	{{clear}}		{{clear}}

← Äldre version		Versionen från 29 november 2016 kl. 15.47
Rad 45:		Rad 45:

	{{khanruta \| [https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-complex-numbers/e/multiplying_complex_numbers Multiply complex numbers]}}		{{khanruta \| [https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-complex-numbers/e/multiplying_complex_numbers Multiply complex numbers]}}
	{{khanruta \| [https://www.khanacademy.org/math/algebra-home/alg-complex-numbers/alg-complex-conjugates-and-dividing-complex-numbers/e/dividing_complex_numbers Divide complex numbers}}		{{khanruta \| [https://www.khanacademy.org/math/algebra-home/alg-complex-numbers/alg-complex-conjugates-and-dividing-complex-numbers/e/dividing_complex_numbers Divide complex numbers]}}
	{{khanruta \| [https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-fractions-2/e/complex-fractions Simplify hairy fractions] }}		{{khanruta \| [https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-fractions-2/e/complex-fractions Simplify hairy fractions] }}