Download 1.1 Write Complex Numbers

1.1
Write Complex Numbers
Vocabulary
• A number r is a square root of a number s
if r2 = s.
• The expression
s is called a radical.
– The symbol
is a radical sign and the
number s beneath the radical sign is the
radicand of the expression.
Vocabulary
• Product Property of
Radicals
ab  a  b
• Quotient Property of
Radicals
a

b
a
b
Vocabulary
• The imaginary unit i is defined as
i  -1
where
i  -1
2
Vocabulary
• A complex number written in standard
form is a number a + bi where a and b are
real numbers.
– The number a is the real part of the complex
number, and the b number is the imaginary
part.
– Example: 2 + 3i
Real
Part
Imaginary
Part
Vocabulary
• If b = 0, then a + bi is an imaginary
number.
• If a = 0 and b = 0, then a + bi is a pure
imaginary number.
– 0 + bi = bi
(there is not an real part…NO “a”)
Vocabulary
• Two complex numbers a + bi and c + di
are equal if and only if a = c and b = d.
• For example, if x + yi = 5 – 3i, then x = 5
and y = -3
Example 1:
• Simplify the expression
a)
8 6
b)
5
36
Example 2:
• Write complex numbers in standard form
a) 25
b)
3
c)
12
d) 4 
16
Example 3:
•
Find real numbers x and y to make the
equation true.
1) 4x – 4yi = 8 – 12i
2) 5x + 3yi = 10 + 18i
Classwork
• Out of your notetaking guide
pg. 4 – 5 ALL