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Example 6.1
Plot in the complex plane, the three points (P , P , P ) representing the com-
2
3
1
plex numbers: z = 1, z = j, z = –1.
1
2
3
Solution: Enter and execute the following commands in the command
window:
z1=1;
z2=j;
z3=-1;
plot(z1,'*')
axis([-2 2 -2 2])
axis('square')
hold on
plot(z2,'o')
plot(z3,'*')
hold off

that is, a complex number in the plot command is interpreted by MATLAB
to mean: take the real part of the complex number to be the x-coordinate and
the imaginary part of the complex number to be the y-coordinate.

6.2.1 Addition
Next, we define addition for complex numbers. The rule can be directly
deduced from analogy of addition of two vectors in a plane: the x-component
of the sum of two vectors is the sum of the x-components of each of the vec-
tors, and similarly for the y-component. Therefore:

If: z = a + jb 1 (6.2)
1
1
and z = a + jb 2 (6.3)
2
2
Then: z + z = (a + a ) + j(b + b ) (6.4)
1 2 1 2 1 2
The addition or subtraction rules for complex numbers are geometrically
translated through the parallelogram rules for the addition and subtraction
of vectors.

Example 6.2
Find the sum and difference of the complex numbers

© 2001 by CRC Press LLC