A.6 Complex
Numbers & Solving
Equations
Imaginary Numbers
i  1
i 3  i
i  1
2


i19  ____
i4  1
i 5  ____
Complex Numbers
Complex numbers are numbers of the form a  bi
where a is called the real part and b is the imaginary part

Complex Numbers
To add complex numbers, add the real parts and add
the imaginary parts together (same for subtraction).
(a  bi)  (c  di)  (a  c)  (b  d)i
(a  bi)  (c  di)  (a  c)  (b  d)i
To multiply complex numbers, follow the usual rules

for multiplying two binomials. DOUBLE DISTRIBUTION!!!


(a  bi)  (c  di)  a(c  di)  bi(c  di)
i 2  1
Complex Numbers
Given the following complex numbers, perform the
indicated operations. w  5  3i
z  1 4i
1) w  z
2) w  z
3) w  z


Complex Numbers
If z  a  bi is a complex number, then its conjugate,
denoted by z , is defined as
z  a  bi  a  bi


zz  a2  b2
Complex Numbers
Let’s find the conjugate of the following complex numbers
and then multiply by the conjugate.
1) z  3 4i
2) z  1 8i
3) z  2i
Complex Numbers
We can apply multiplying conjugates to quotients of complex
numbers. Let’s write the following in standard form!
2  3i
4  3i

Complex Numbers
Given the following complex numbers, perform the
indicated operations. w  2  3i
z  5  2i
1) w  z
2) w  z
3) w  z
w
4)
z


A.6 Complex
Numbers & Solving
Equations
Homework#8:
p.1008 #9 – 45 Odd