1. Lab No.08
Complex exponentials and phasors
Designed by : Dawar Awan
dawar@cecos.edu.pk
CECOS College of Engineering and IT
March – July 2012

2. Complex numbers
 Complex number , z = (3,4) = 3+4i
 ‘z’ can be defined in MatLab as , z=3+4i;
 Now, try the following commands.
real(z)
imag(z)
abs(z)
angle(z)
conj(z)
CECOS College of Engineering and IT
Real part of z
imaginary part of z
magnitude or modulus of z
phase or angle of z
conjugate of z
March – July 2012

3. Task
1. for z = 1+2i+3 , find the real and imaginary parts of z.
2. for z = 2+3i = Aejθ , find A and θ.
3. for z1 = 1+2i and z2 = 2+3i and z3 = z1.z2 = BejФ , find B
and Ф.
CECOS College of Engineering and IT
March – July 2012

4. Complex exponential signals
 A complex exponential signal is defined as
x(t)=Aej(wt+Ф)
 where
A= amplitude
w= frequency in rad/sec
Ф= phase
 According to Euler’s formula
Aej(wt+Ф) = Acos(wt+Ф) + jAsin(wt+Ф)
CECOS College of Engineering and IT
March – July 2012

5. Task
 In MATLAB x(t)=Aej(wt+Ф) is defined as
x=A*exp(i*(wt+ Ф))
 For the complex exponential signal x(t), verify the
Euler’s relation ship by plotting the real and imaginary
parts of x(t), for x(t)= 2ej(4πt)
 Plot the real and imaginary parts of the conjugate of x(t)
CECOS College of Engineering and IT
March – July 2012

6. Phasor addition
 Sinusoids having same frequency can be added using
their phasors
 Phasor representation of x(t)=Acos(2πft + ф), is X=Aejф
 Example :
x1(t)=1.7cos(2π10t+70π/180) ------- X1=1.7ej 70 π/180
x2(t)=1.9cos(2π10t+200π/180) ------- X2=1.9ej 200 π/180
To find x3(t)=x1(t)+x2(t) , we first add their phasors
CECOS College of Engineering and IT
March – July 2012

7. Phasor addition
X3= X1 + X2
X3= 1.7ej 70 π/180 + 1.9ej 200 π/180
Convert them to rectangular form, add them, and then
convert back to polar form (Task)
X3 = 1.532ej 141.79 π/180
x3(t) =1.532cos(2π10t + 141.79π/180)
CECOS College of Engineering and IT
March – July 2012

8. Task
 Verify the phasor addition graphically, by showing that
1.7cos(2π10t+70π/180) + 1.9cos(2π10t+200π/180)
= 1.532cos(2π10t + 141.79π/180)
CECOS College of Engineering and IT
March – July 2012