Post on 05-Jan-2016
Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig.
Aim: How do we add and subtract complex numbers?
Do Now:
Simplify:
3 45 125 2 20
3 9 5 25 5 2 4 5
9 5 5 5 4 5
10 5
Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig.
Adding Complex Numbers
(2 + 3i) + (5 + i) = (2 + 5) + (3i + i) = 7 + 4i
In general, addition of complex numbers:(a + bi) + (c + di) = (a + c) + (b + d)i
Find the sum of
(5 36) and (3 16)
(5 36) (3 16)
(5 i 36) (3 i 16)
(5 6i) (3 4i)
(5 3) (6i 4i)
8 2i
Combine the real parts and the imaginary parts separately.
convert tocomplex numbers
combine reals andimaginary parts separately
Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig.
Subtracting Complex Numbers
(1 + 3i) – (3 + 2i) = (1 + 3i) + (-3 – 2i) = -2 + i
Subtract
6 2i 3 from 5 3i 3
5 3i 3 6 2i 3
What is the additive inverse of 2 + 3i?-(2 + 3i) or -2 – 3i
Subtraction is the addition of an additive inverse
5 3i 3 6 2i 3
5 ( 6) ( 3i 3) 2i 3
1 i 3
In general, subtraction of complex numbers:(a + bi) – (c + di) = (a – c) + (b – d)i
change to additionproblem
combine reals andimaginary parts separately
Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig.
x1 2 3 4 5 6-5 -4 -3 -2 -1 0
i
2i
3i
4i
5i
-4i
-3i
-2i
-i
-5i
-6i
yi
Adding Complex Numbers Graphically
(2 + 3i)
(2 + 3i) + (3 + 0i)
(3 + 0i)
(5 + 3i)
= (2 + 3) + (3i + 0i) = = 5 + 3i
vector: 2 + 3i
vector: 3 + 0i
vector: 5 + 3i
Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig.
Adding Vectors
Vector - a directed line segment that represents directed force notation: OS
R
The vectors that represent the applied forcesform two adjacent sides of a parallelogram, and the vector that represents the resultantforce is the diagonal of this parallelogram.
O
P S
resultant force
Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig.
x1 2 3 4 5 6-5 -4 -3 -2 -1 0
i
2i
3i
4i
5i
-4i
-3i
-2i
-i
-5i
-6i
yi
Subtracting Complex Numbers Graphically
(1 + 3i)
(1 + 3i) – (3 + 2i)
(3 + 2i)
= (1 + 3i) + (-3 – 2i) = -2 + i
(-3 – 2i)
(-2 + i)
The vector representing the additive inverse isthe image of the vector reflected through the origin. Or the image under a rotation aboutthe origin of 1800.
Aim: Add & Subtract Complex Numbers Course: Adv. Alg. & Trig.
Model Problems
Add/Subtract and simplify:
(10 + 3i) + (5 + 8i)
(4 – 2i) + (-3 + 2i)
2
3
i
4
1
6
i
2
1 80 3 20 Express the difference of
1 80 2 162 in form a + bi
= 15 + 11i
= 1
4
6
i
4
1
6
2i
4
5
6
3i
4
4 6i 5
3 4 5 9 2 i