First, find the sum or difference of the real parts of the
complex number. Then, to find the sum or difference of the
imaginary numbers, add or subtract the coefficients of i. The sum
or difference of two complex numbers can be wholly real (having
only real parts), wholly imaginary (having only imaginary parts),
or complex (having both real and imaginary parts). 4.3.2: Adding
and Subtracting Complex Numbers2
Slide 4
Is (5 + 6i 9 ) (5 + 3i 15 ) wholly real or wholly imaginary, or
does it have both a real and an imaginary part? 4.3.2: Adding and
Subtracting Complex Numbers3
Slide 5
Two expressions, 6i 9 and 3i 15, contain i n. Divide each power
of i by 4 and use the remainder to simplify i n. 9 4 = 2 remainder
1, so 9 = 2 4 + 1. i 9 = i 2 4 i 1 = i 15 4 = 3 remainder 3, so 15
= 3 4 + 3. i 15 = i 3 4 i 3 = i 4.3.2: Adding and Subtracting
Complex Numbers4
Slide 6
Replace each occurrence of i n in the expressions with the
simplified versions, and replace the original expressions in the
difference with the simplified expressions. 6i 9 = 6 (i) = 6i 3i 15
= 3 (i) = 3i (5 + 6i 9 ) (5 + 3i 15 ) = (5 + 6i) [5 + (3i)] 4.3.2:
Adding and Subtracting Complex Numbers5
Slide 7
Distribute the difference through both parts of the complex
number. Find the sum or difference of the real parts. 5 5 = 0 Find
the sum or difference of the imaginary parts. 6i + 3i = 9i 4.3.2:
Adding and Subtracting Complex Numbers6
Slide 8
Find the sum of the real and imaginary parts. 0 + 9i = 9i Use
the form of the sum to determine if it is wholly real or wholly
imaginary, or if it has both a real and an imaginary part. 9i has
only an imaginary part, 9i, so the difference is wholly imaginary.
4.3.2: Adding and Subtracting Complex Numbers7
Slide 9
Is (12 I 20 ) + (18 4i 18 ) wholly real or wholly imaginary, or
does it have both a real and an imaginary part? 4.3.2: Adding and
Subtracting Complex Numbers8