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Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition C 7 Copyright © Orchard Publications Exponential and Polar Forms of Complex Numbers x=3+j*4; magx=abs(x); thetax=angle(x)*180/pi; disp(magx); disp(thetax) 5 53.1301 Check with the Simulink Complex to Magnitude Angle block * shown in the Simulink model of Figure C.3. Figure C.3. Simulink model for Example C.6a b. The real and imaginary components of this complex number are shown in Figure C.4. Figure C.4. The components of Then, Check with MATLAB: y= 1+j*2; magy=abs(y); thetay=angle(y)*180/pi; disp(magy); disp(thetay) 2.2361 116.5651 c. The real and imaginary components of this complex number are shown in Figure C.5. * For a detailed description and examples with this and other related transformation blocks, please refer to Intro- duction to Simulink with Engineering Applications, ISBN 0 9744239 7 1, Section 8.3, Chapter 8, Page 8 24, and Section 19.8, Chapter 19, Page 19 27. Re Im 2 1 116.6 ° 63.4 ° 5 1 j2 + 1 + 1 2 2 2 + e j 2 1 ----- 1 tan   5e j116.6 ° 51 1 6 . 6 ° == =

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A Review of Complex Numbers C 8 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications Figure C.5. The components of Then, Check with MATLAB: v= 2 j*1; magv=abs(v); thetav=angle(v)*180/pi; disp(magv); disp(thetav) 2.2361 -153.4349 d. The real and imaginary components of this complex number are shown in Figure C.5. Figure C.6. The components of Then, Check with MATLAB: w=4 j*3; magw=abs(w); thetaw=angle(w)*180/pi; disp(magw); disp(thetaw) 5 -36.8699 Re Im 2 1 206.6 ° 153.4 °( Measured 26.6 ° Clockwise) 5 2 j 2 j 12 2 1 2 + e j 1 2 ----- 1 tan   5e j206.6 ° == 52 0 6 . 6 ° j1 5 3 . 4 () ° 51 5 3 . 4 ° = Re Im 4 3 5 323.1× 36.9× 4 j3 4j 34 2 3 2 + e j 3 4 1 tan j323.1 ° 53 2 3 . 1 ° j36.9 ° 6 . 9 ° =
Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition C 9 Copyright © Orchard Publications Exponential and Polar Forms of Complex Numbers Example C.7 Express the complex number in exponential and in rectangular forms.

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