aim: add & subtract complex numbers course: adv. alg. & trig. aim: how do we add and...

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


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


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


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


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


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.


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

aim: add & subtract complex numbers course: adv. alg. & trig. aim: how do we add and...

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