Beginning Algebra, 11th Edition

OBJECTIVE 2 Add and subtract complex numbers. Adding and subtracting

complex numbers is similar to adding and subtracting binomials. To add complex

numbers, add their real parts and add their imaginary parts. To subtract complex

numbers, use the definition of subtraction and add.

576 CHAPTER 9 Quadratic Equations

NOW TRY
EXERCISE 2
Add or subtract.

(a)

(b) 1 - 2 - i 2 - 11 - 3 i 2

13 + 5 i 2 + 1 - 4 - 2 i 2

NOW TRY ANSWERS

2. (a)- 1 + 3 i (b)- 3 + 2 i

Adding and Subtracting Complex Numbers

Add or subtract.

(a)

Add real parts.

Add imaginary parts.

Standard form

(b)

(c)

Definition of subtraction

Properties of real numbers

Add and subtract.

(d)

Properties of real numbers

=- 5 + 2 i Subtract real parts. NOW TRY

= 1 - 1 - 42 + 2 i

1 - 1 + 2 i 2 - 4

= 6 + 5 i

= 12 + 42 + 16 - 12 i

= 12 + 6 i 2 + 14 - i 2

12 + 6 i 2 - 1 - 4 +i 2

=- 2 + 2 i

=- 2 + 13 - 12 i -i=- 1 i

3 i+ 1 - 2 - i 2

= 9 - 2 i

= 12 + 72 + 1 - 6 + 42 i

12 - 6 i 2 + 17 + 4 i 2

EXAMPLE 2

OBJECTIVE 3 Multiply complex numbers.We multiply complex numbers as

we do polynomials. Since by definition, whenever appears, we replace it

with . 1

i^2 =- 1 i^2

Multiplying Complex Numbers

Find each product.

(a)

Distributive property

Multiply.

Standard form

(b)

Use the FOIL method.

Multiply.

Combine terms;

Multiply.

= 23 + 14 i Add.

= 8 + 14 i+ 15

= 8 + 14 i- 151 - 12 i 2 =- 1

= 8 + 20 i- 6 i- 15 i^2

= 4122 + 415 i 2 + 1 - 3 i 22 + 1 - 3 i 25 i

14 - 3 i 212 + 5 i 2

= 15 + 6 i

= 6 i+ 15

= 6 i- 151 - 12 i^2 =- 1

= 6 i- 15 i^2

3 i 12 - 5 i 2

EXAMPLE 3

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