Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Please assist with question P-2.8. With details on how to do it. Thank you.

### Complex Numbers and MATLAB #### P-2.7 Simplify the following expressions: (a) \( 3e^{j\pi/3} + 4e^{-j\pi/6} \) (b) \( (\sqrt{3} - j3)^{10} \) (c) \( (\sqrt{3} - j3)^{-1} \) (d) \( (\sqrt{3} - j3)^{1/3} \) (e) \( \Re \left\{ je^{-j\pi/3} \right\} \) **Instructions**: Give the answers in both Cartesian form (\( x + jy \)) and polar form (\( re^{j\theta} \)). #### P-2.8 MATLAB Plotting a Sinusoidal Signal **Scenario**: Suppose that MATLAB is used to plot a sinusoidal signal. The following MATLAB code generates the signal and makes the plot. Derive a formula for the signal; then without running the program, draw a sketch of the plot that will be done by MATLAB. ```matlab dt = 1/1000; tt = -0.15 : dt : 0.15; Fo = 7; zz = 15*exp(j*(2*pi*Fo*(tt + 0.875))); xx = real( zz ); plot( tt, xx ), grid on title('SECTION of a SINUSOID') xlabel('TIME (s)') ``` **Explanation**: This code snippet generates a section of a sinusoidal wave. Let’s break down the code to derive the formula for the signal and sketch the plot. 1. **Line 1**: ```matlab dt = 1/1000; ``` This sets the time step \( dt \) to 0.001 seconds. 2. **Line 2**: ```matlab tt = -0.15 : dt : 0.15; ``` This creates a time vector \( tt \) from -0.15 to 0.15 seconds in increments of \( dt \). 3. **Line 3**: ```matlab Fo = 7; ``` This sets the frequency \( F_o \) to 7 Hz. 4. **Line 4**: ```matlab zz = 15*exp(j*(2*pi*Fo
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Transcribed Image Text:### Complex Numbers and MATLAB #### P-2.7 Simplify the following expressions: (a) \( 3e^{j\pi/3} + 4e^{-j\pi/6} \) (b) \( (\sqrt{3} - j3)^{10} \) (c) \( (\sqrt{3} - j3)^{-1} \) (d) \( (\sqrt{3} - j3)^{1/3} \) (e) \( \Re \left\{ je^{-j\pi/3} \right\} \) **Instructions**: Give the answers in both Cartesian form (\( x + jy \)) and polar form (\( re^{j\theta} \)). #### P-2.8 MATLAB Plotting a Sinusoidal Signal **Scenario**: Suppose that MATLAB is used to plot a sinusoidal signal. The following MATLAB code generates the signal and makes the plot. Derive a formula for the signal; then without running the program, draw a sketch of the plot that will be done by MATLAB. ```matlab dt = 1/1000; tt = -0.15 : dt : 0.15; Fo = 7; zz = 15*exp(j*(2*pi*Fo*(tt + 0.875))); xx = real( zz ); plot( tt, xx ), grid on title('SECTION of a SINUSOID') xlabel('TIME (s)') ``` **Explanation**: This code snippet generates a section of a sinusoidal wave. Let’s break down the code to derive the formula for the signal and sketch the plot. 1. **Line 1**: ```matlab dt = 1/1000; ``` This sets the time step \( dt \) to 0.001 seconds. 2. **Line 2**: ```matlab tt = -0.15 : dt : 0.15; ``` This creates a time vector \( tt \) from -0.15 to 0.15 seconds in increments of \( dt \). 3. **Line 3**: ```matlab Fo = 7; ``` This sets the frequency \( F_o \) to 7 Hz. 4. **Line 4**: ```matlab zz = 15*exp(j*(2*pi*Fo
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