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Addition and Subtraction of Phasors

y
jA

(
)
jjA = j A = – A A
2
x
2
)
(
j – jA = j – A = A
(
)
3
j – A = j A = – jA
Figure 3.7. The j operator
A complex number is the sum (or difference) of a real number and an imaginary number. For
b
a
example, the number A = a + jb where and are both real numbers, is a complex number.
A
Then, a = Re A{} and b = Im A{} where Re A{} denotes real part of , and b = Im A{} the
imaginary part of . When written as A = a + jb , it is said to be expressed in rectangular form.
A
Since in engineering we use complex quantities as phasors, henceforth any complex number will
be referred to as a phasor.

A
By definition, two phasors and where A = a + jb and B = c + jd , are equal if and only if
B
their real parts are equal and also their imaginary parts are equal. Thus, A = B if and only if
a = c and b = . d

3.5 Addition and Subtraction of Phasors

The sum of two phasors has a real component equal to the sum of the real components, and an
imaginary component equal to the sum of the imaginary components. For subtraction, we change
the signs of the components of the subtrahend and we perform addition. Thus, if A = a + jb and
B = c + jd , then

)
(
A + B = ( a + c + jb + d )
and
(
)
A – B = ( a – c + jb – d )

Example 3.3

It is given that A = 3 + j4 , and B = 4 – j2 . Find A + B and A – B

Solution:

Numerical Analysis Using MATLAB® and Excel®, Third Edition 3−11
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