7.10 c omplex n umbers a ddition and s ubtraction
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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
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