5.6 Complex Numbers

Solve the following quadratic:

x2 + 1 = 0

Is this quadratic factorable?

What does its graph look like?

x 2 1

x 2 1

x 1

But I thought that you could not take the square root of a negative number???

1ii is called an imaginary number because many thought that the square root of an imaginary number was impossible.

Complex Numbers

Complex numbers are the combination of real numbers and imaginary numbers.

Complex numbers are written in the form:

a bi

Real Part

Imaginary Part

Simplifying Complex Numbers

16 i4

32 24 i24

216 i66

150 i65

1002 i20

2002 i220

Simplifying Complex Numbers

5 16

5 4 1

5 4i

32 7

7 4 2

7 4 2i

108 6

6 6 3i

75 25

25 5 3i

273752 ii 39310 i319

Solve the quadratic equation

23 10 26x

363 2 x122 x

122 x

12ix

32ix

Adding and Subtracting(add or subtract the real parts, then add or

subtract the imaginary parts)

Ex: )33()21( ii )32()31( ii

i52

Ex: )73()32( ii )73()32( ii

i41

Ex: )32()3(2 iii )32()23( iii

i21

Ex: )3( ii 23 ii )1(3 i

i31

Multiplying complex numbers

Simplify the following:

3 2i 4 5i

12 15i 8i 10i2

110712 i

12 7i 10

22 7i

5 7i 2 3i

10 15i 14i 21i2

1212910 i 212910 i

i2911

Multiplying complex numbers

Simplify the following:

3 i 2

9 6i i2

8 6i

5 7i 5 7i

25 49i2

25 4974