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1 Useful functions in MATLAB related to complex numbers MATLAB functionDescriptionExample (MATLAB outputs in red) real(x)Real part of complex number A = 3 + 4i; X = real(A) X = 3 imag(x)Imaginary part of complex number A = 3 + 4i; X = imag(A) X = 4 abs(x)Magnitude of a complex number X = abs(3+4i) X = 5 angle(x)Angle of a complex number in radians Alpha = angle(3+4i)*180/pi alpha = conj(x)Complex conjugate of complex number A = 3+4i A = i X = conj(A) X = i Complex Numbers in MATLAB We will begin this section by looking at several useful functions in MATLAB related to complex numbers. EGR 272 – Complex Numbers and AC Circuits using MATLAB

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MATLAB functionDescriptionExample (MATLAB outputs in red) [theta, r] = cart2pol(x, y)Converts from rectangular to polar form where theta is in radians [Radians,Mag]=cart2pol(3,4) Radians = Mag = 5 Degrees=Radians*180/pi Degrees = Note: so 3 + 4i = [x, y] = pol2cart(theta, r)Converts from polar to rectangular form where theta is in radians [a,b]=pol2cart(30*pi/180,10) a = b = Note: so = i complex(a,b)Form complex data from real and imaginary parts X = complex(3,4) X = i A = [3;-3;-3;3]; B = [4;4;-4;-4]; C = complex(A,B) C = i i i i Useful functions in MATLAB related to complex numbers 2 EGR 272 – Complex Numbers and AC Circuits using MATLAB

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Useful operations in MATLAB related to complex numbers MATLAB operationsDescriptionExample (MATLAB outputs in red) Exponentiation(^)Raise a complex number to a power X = (1+2i)^2 X = i Arithmetic operations -Addition (+) -Subtraction (-) -Multiplication (*) -Division (/) Converts from polar to rectangular form where theta is in radians A=3+4i; B=2+6i; A+B ans = i A-B ans = i A*B ans = i A/B ans = i Exponential polar formX = 10*exp(30i*pi/180) X = i [Real,Imag]=pol2cart(30*pi/180,10) Real = Imag = Note: So 10e j30 = EGR 272 – Complex Numbers and AC Circuits using MATLAB

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Printing Complex Numbers in MATLAB Some options for printing complex numbers in MATLAB include: 1)Do not suppress printing and accept the default format (rectangular form): 2)Display using fprintf (not perfect, but may be sufficient in some cases) 4 EGR 272 – Complex Numbers and AC Circuits using MATLAB

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Printing Complex Numbers in MATLAB Some options for printing complex numbers in MATLAB include: 3.Convert complex number to a string using num2str( ) and print using %s: 5 EGR 272 – Complex Numbers and AC Circuits using MATLAB

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AC Circuit Analysis Procedure: 1) Draw the phasor circuit (showing voltage and current sources as phasors and using complex impedances for the components). 2) Analyze the circuit in the same way that you might analyze a DC circuit. 3) Convert the final phasor result back to the time domain. Application of Complex Numbers: AC Circuit Analysis (Phasor Analysis) Example: Use the total current using phasor analysis by hand. 6 EGR 272 – Complex Numbers and AC Circuits using MATLAB Solution: See next slide

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7 EGR 272 – Complex Numbers and AC Circuits using MATLAB 50 0 V j25-j50 j20 I Solution: phasor circuit:

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Example: Use MATLAB to solve for the total phasor current. 8 EGR 272 – Complex Numbers and AC Circuits using MATLAB

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