1.4 COMPLEX NUMBERS

1.4 COMPLEX NUMBERS

MATLAB allows operations involving complex numbers. Complex numbers

are entered using function i or j. For example, a number z = 2 + j2 may be

entered in MATLAB as

z = 2+2*i

or

z = 2+2*j

Also, a complex number za

za = 2 2 exp[(π / 4) j]

can be entered in MATLAB as

za = 2*sqrt(2)*exp((pi/4)*j)

It should be noted that when complex numbers are entered as matrix elements

within brackets, one should avoid any blank spaces. For example,

y = 3 + j4 is represented in MATLAB as

y = 3+4*j

If spaces exist around the + sign, such as

u= 3 + 4*j

MATLAB considers it as two separate numbers, and y will not be equal to u.

If w is a complex matrix given as

w =

1 1 2 2

3 2 4 3

+ −

+ +



 



 

j j

j j

then we can represent it in MATLAB as

w = [1+j 2-2*j; 3+2*j 4+3*j]

which will produce the result

w =

1.0000 + 1.0000i 2.0000 - 2.0000i

3.0000 + 2.0000i 4.0000 + 3.0000i

If the entries in a matrix are complex, then the “prime” (‘) operator produces

the conjugate transpose. Thus,

wp = w'

will produce

wp =

1.0000 - 1.0000i 3.0000 - 2.0000i

2.0000 + 2.0000i 4.0000 - 3.0000i

For the unconjugate transpose of a complex matrix, we can use the point transpose

(.’) command. For example,

wt = w.'

will yield

© 1999

wt =

1.0000 + 1.0000i 3.0000 + 2.0000i

2.0000 - 2.0000i 4.0000 + 3.0000i