Adding & Subtracting
Adding and Subtracting Imaginary Numbers
We add and subtract imaginary numbers in the same manner as other radicals.
1. Combine like terms.
2. Add the real number parts together
3. Add the imaginary parts together
Example #1
Add these imaginary numbers: (3 +4i) + (-5 + 8i)
Use commutative & associative properties to group like terms together
(3 +4i) + (-5 + 8i) = (3 + -5) + ( ___ + ___ )
Add/Combine like terms
(3 + 4i) + (-5 + 8i) = ___ + ___
Example #2
Subtract these imaginary numbers: (-6 + 3i) - (5 - i)
(-6 + 3i) - (5 - i) = (-6 + 3i) + (-5 + i)
Rewrite, even if you do this in your head
(-6 + 3i) - (5 - i) = (-6 ___ ) + ( ___ + i)
Use commutative & associative properties to group like terms together
(-6 + 3i) - (5 - i) = ___ + ___
add/combine like terms
Example #3
Critique this problem: (7 - 9i) - (4 + 10i) = 3 + i
It is not a good idea to leave out too much work.
(7 - 9i) - (4 + 10i) should be rewritten as (7 - 9i) + (-4 -10i)
Then it is easier to see that it should be -9i + 10i = -19i. The answer would be 3 - 19i.
