7.10 COMPLEX NUMBERSADDITION AND SUBTRACTION

A number is in the form a represents the part b represents the part

Definition of Addition in the Complex Numbers:

If a, b, c, and d are real numbers, then

a + bicomplexreal

imaginary

a + bi( ) + c+ di( ) = a+ c( ) + b+ d( )i

Definition For any real numbers a and b, the

of is and vice versa.

If a complex number is called z, its complex conjugate is called .

a + bi a −bi

z

complexconjugate

Let

a =2 +7i b =−3−5i

c =10 −9i d =3i

e =

12

−23

i f =

34

+16

i

g =

38

+512

i h =

56

SIMPLIFY.

1. 2. a + c c −d

SIMPLIFY.

3. 4. d −a f −g

SIMPLIFY.

5. 6. e −g e − f

SIMPLIFY.

7. 8. f + f g −g

Theorem: If a, b, c, and, d are real numbers, then

if and only if and . a + bi =c+ di

a =c b =d

9.

Solve for x and y, where x and y are real numbers.

2y + yi =3i + xi −x

10.

Solve for x and y, where x and y are real numbers.

x −y( ) + x+ y( )i =4 +10i