1.1 Write Complex Numbers

Vocabulary

• A number r is a square root of a number s if r2 = s.

• The expression is called a radical.

– The symbol is a radical sign and the number s beneath the radical sign is the radicand of the expression.

s

Vocabulary

• Product Property of Radicals

• Quotient Property of Radicals

ab a b a a

b b

Vocabulary

• The imaginary unit i is defined as

2

-1

-1

i

where

i

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)

b)

8 6

5

36

Example 2:

• Write complex numbers in standard forma)

b)

c)

d)

25

3

12

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