Aufgaben:Exercise 1.3: Calculating with Complex Numbers - Revision history

Guenter at 12:28, 24 May 2021

2021-05-24T12:28:05Z

Guenter at 12:26, 24 May 2021

2021-05-24T12:26:51Z

Guenter at 12:23, 24 May 2021

2021-05-24T12:23:09Z

Guenter at 16:17, 17 May 2021

2021-05-17T16:17:16Z

Guenter: Guenter moved page Aufgaben:Exercise 1.3: Calculating With Complex Numbers to Aufgaben:Exercise 1.3: Calculating with Complex Numbers

2021-04-12T11:38:44Z

Guenter moved page Exercise 1.3: Calculating With Complex Numbers to Exercise 1.3: Calculating with Complex Numbers

Guenter at 11:36, 12 April 2021

2021-04-12T11:36:26Z

Guenter at 15:16, 9 April 2021

2021-04-09T15:16:45Z

Guenter at 15:01, 9 April 2021

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Guenter at 14:52, 9 April 2021

2021-04-09T14:52:57Z

Noah at 09:11, 26 March 2021

2021-03-26T09:11:42Z

← Older revision		Revision as of 12:28, 24 May 2021
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−	{{quiz-Header\|Buchseite=~~Signaldarstellung~~/Calculating_With_Complex_Numbers}}	+	{{quiz-Header\|Buchseite=Signal_Representation/Calculating_With_Complex_Numbers}}

	[[File:P_ID800_Sig_A_1_3.png\|right\|frame\|Considered numbers <br>in the complex plane]]		[[File:P_ID800_Sig_A_1_3.png\|right\|frame\|Considered numbers <br>in the complex plane]]

← Older revision		Revision as of 12:26, 24 May 2021
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−	{{quiz-Header\|Buchseite=Signaldarstellung/~~Calculating with Complex Numbers~~}}	+	{{quiz-Header\|Buchseite=Signaldarstellung/Calculating_With_Complex_Numbers}}

	[[File:P_ID800_Sig_A_1_3.png\|right\|frame\|Considered numbers <br>in the complex plane]]		[[File:P_ID800_Sig_A_1_3.png\|right\|frame\|Considered numbers <br>in the complex plane]]

← Older revision		Revision as of 12:23, 24 May 2021
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−	{{quiz-Header\|Buchseite=Signaldarstellung/Calculating ~~With~~ Complex Numbers}}	+	{{quiz-Header\|Buchseite=Signaldarstellung/Calculating with Complex Numbers}}

	[[File:P_ID800_Sig_A_1_3.png\|right\|frame\|Considered numbers <br>in the complex plane]]		[[File:P_ID800_Sig_A_1_3.png\|right\|frame\|Considered numbers <br>in the complex plane]]

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 {{quiz-Header|Buchseite=Signaldarstellung/Calculating With Complex Numbers}}
-[[File:P_ID800_Sig_A_1_3.png|right|frame|Considered numbers in the complex plane]]
+[[File:P_ID800_Sig_A_1_3.png|right|frame|Considered numbers <br>in the complex plane]]
 The diagram to the right shows some points in the complex plane, namely

← Older revision		Revision as of 11:36, 12 April 2021
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−	[[Category:Signal Representation: Exercises\|^1.3 Calculating ~~With~~ Complex Numbers^]]	+	[[Category:Signal Representation: Exercises\|^1.3 Calculating with Complex Numbers^]]

← Older revision	Revision as of 11:38, 12 April 2021
(No difference)

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 ''Notes:''
 *This exercise belongs to the chapter&nbsp;[[Signal_Representation/Calculating_With_Complex_Numbers|Calculating with Complex Numbers]].
-*The topic is also covered in the (German language) learning video <br> &nbsp; &nbsp;  &nbsp;[[Rechnen_mit_komplexen_Zahlen_(Lernvideo)|Rechnen mit komplexen Zahlen]] &nbsp; &rArr; &nbsp; "Arithmetic operations involving complex numbers".
+*The topic of this task is also covered in the (German language) learning video <br> &nbsp; &nbsp;  &nbsp;[[Rechnen_mit_komplexen_Zahlen_(Lernvideo)|Rechnen mit komplexen Zahlen]] &nbsp; &rArr; &nbsp; "Arithmetic operations involving complex numbers".

@@ Line 90: / Line 90: @@
 ::<math>z_2^2 =  2^2 \cdot{\rm e}^{{\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm} 270^{ \circ}}= 4 \cdot {\rm e}^{-{\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm} 90^{ \circ}}=-4 \cdot {\rm j}.</math>
-*Accordingly, the following applies to the square of&nbsp; <math>z_3</math>:&nbsp;:
+*Accordingly, the following applies to the square of&nbsp; <math>z_3</math>:
 ::<math>z_3^2 =  (-{\rm j})^2 = -1.</math>

@@ Line 15: / Line 15: @@
 :$$z_8 = {\rm e}^{\hspace{0.05cm}z_2} + {\rm e}^{\hspace{0.05cm}z_2^{\star}}.$$
 ''Notes:''
-*This exercise belongs to the chapter&nbsp;[[Signal_Representation/Calculating_With_Complex_Numbers|Calculating With Complex Numbers]].
+*This exercise belongs to the chapter&nbsp;[[Signal_Representation/Calculating_With_Complex_Numbers|Calculating with Complex Numbers]].
-*The topic is also covered in the teaching video&nbsp;[[Rechnen_mit_komplexen_Zahlen_(Lernvideo)|Rechnen mit komplexen Zahlen]]&nbsp;.
+*The topic is also covered in the (German language) learning video <br> &nbsp; &nbsp;  &nbsp;[[Rechnen_mit_komplexen_Zahlen_(Lernvideo)|Rechnen mit komplexen Zahlen]] &nbsp; &rArr; &nbsp; "Arithmetic operations involving complex numbers".
@@ Line 37: / Line 34: @@
-{What is the value of the random variable&nbsp; <math>z_4 = z_2^2 + z_3^2 = x_4 + {\rm j} \cdot y_4</math>?
+{What is the value of the complex quantity&nbsp; <math>z_4 = z_2^2 + z_3^2 = x_4 + {\rm j} \cdot y_4</math>?
 |type="{}"}
 <math> x_4 \ =\  </math> { -1.01--0.99 }
@@ Line 48: / Line 45: @@
 <math> y_5  \ =\  </math> { -0.36--0.35 }
-{<math>z_6</math>&nbsp; is the square root of&nbsp; <math>z_3</math>&nbsp;. Therefore <math>z_6</math>&nbsp; has two solutions with the magnitude&nbsp; <math>|z_6| = 1</math>. <br>Give the two possible phase angles of&nbsp; <math>z_6</math>&nbsp;.
+{<math>z_6</math>&nbsp; is the square root of&nbsp; <math>z_3</math>.&nbsp; Therefore <math>z_6</math>&nbsp; has two solutions with the magnitude&nbsp; <math>|z_6| = 1</math>. <br>Give the two possible phase angles of&nbsp; <math>z_6</math>&nbsp;.
 |type="{}"}
 <math> \phi_6 \ ({\rm between\hspace{0.1cm} 0^{\circ}  \hspace{0.1cm}and \hspace{0.1cm} +\hspace{-0.15cm}180^{\circ} \hspace{0.1cm}deg}) \hspace{0.2cm} =\ </math>    { 133-137 } $\ \text{deg}$
@@ Line 60: / Line 57: @@
-{Compute the complex quantity&nbsp;  <math>z_8 =  {\rm e}^{z_2} +  {\rm e}^{z_2^{\ast}} = x_8 + {\rm j}\cdot y_8</math>&nbsp;.
+{Calculate the complex quantity&nbsp;  <math>z_8 =  {\rm e}^{z_2} +  {\rm e}^{z_2^{\ast}} = x_8 + {\rm j}\cdot y_8</math>&nbsp;.
 |type="{}"}
 <math> x_8 \ =\  </math> { 0.07-0.08 }