5.4

Complex Numbers

Let’s see… Can you find the square root of a number?

4

1

40025A.

E.D.

C.B.75

16

90

So What’s new?

To find the square root of negative numbers you need to use imaginary numbers.• i is the imaginary unit

• i2 = -1

• i = 1

Square Root Property

For any real number x, if x2 = n, then x = ± n

What about the square root of a negative number?

184

1

81

32

455125xE.D.

C.B.A.

Let’s Practice With i

Simplify -2i (7i)

(2 – 2i) + (3 + 5i)

i45

i31

1510

A.

B.

C.

D.

E.

Solve

3x2 + 48 = 0

4x2 + 100 = 0

x2 + 4= 0

A.

B.

C.

5.4 Day #2 More with Complex Numbers

Multiply• (3 + 4i) (3 – 4i)

• (1 – 4i) (2 + i)

• (1 + 3i) (7 – 5i)

• (2 + 6i) (5 – 3i)

*Reminder: You can’t have i in the denominator

Divide 3i 5 + i 2 + 4i 2i

-2i 4 - i 3 + 5i 5i

2 + i 1 - i

E.

D.

C.

B.

A.