A.6 Complex Numbers & Solving

Equations

Imaginary Numbers

1i

i2 1

i3 i

i4 1 ____5 i

____19 i

Complex numbers are numbers of the form

where a is called the real part and b is the imaginary part

Complex Numbers

a bi

Complex NumbersTo 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.

(a bi)(c di)a(c di) bi(c di)

DOUBLE DISTRIBUTION!!!

i2 1

Given the following complex numbers, perform the indicated operations.

Complex Numbers

w z

w 5 3i

z 1 4i

w z

w z

1)

2)

3)

If is a complex number, then its conjugate, denoted by , is defined as

Complex Numbers

z a bi

z

z a bi a bi

zz a2 b2

Let’s find the conjugate of the following complex numbers and then multiply by the conjugate.

Complex Numbers

z 3 4i

z 1 8i

z 2i

1)

2)

3)

We can apply multiplying conjugates to quotients of complex numbers. Let’s write the following in standard form!

Complex Numbers

2 3i4 3i

Complex NumbersGiven the following complex numbers, perform the indicated operations.

w 2 3i

z 5 2i

w z

w z

w z

1)

2)

3)

wz

4)

Homework#8: p.1008 #9 – 45 Odd

A.6 Complex Numbers & Solving

Equations