I hate to ask it…I hate to ask it…

How do we multiply and divide these things?

How do we multiply and divide these things?

Before we beginBefore we begin

Remember multiplying binomials? (Binomials are things with two terms)

Ex. (x – 2), (y + 7), (3 + 5z) To multiply two binomials, we had to

multiply each part of each binomial FOIL

First, Outer, Inner, Last

Remember multiplying binomials? (Binomials are things with two terms)

Ex. (x – 2), (y + 7), (3 + 5z) To multiply two binomials, we had to

multiply each part of each binomial FOIL

First, Outer, Inner, Last

Multiplying binomialsMultiplying binomials

(x+3)(x-5) Multiply first terms: x*x=x2

Multiply outer terms: x*(-5)=-5x Multiply inner terms: 3*x=3x Multiply last terms: 3*(-5)=-15 Add them all together: x2-5x+3x-15 Combine like terms: x2-2x-15

(x+3)(x-5) Multiply first terms: x*x=x2

Multiply outer terms: x*(-5)=-5x Multiply inner terms: 3*x=3x Multiply last terms: 3*(-5)=-15 Add them all together: x2-5x+3x-15 Combine like terms: x2-2x-15

Important casesImportant cases

Squaring binomial (x+y)(x+y)=(x+y)2

=x2+2xy+y2

Conjugates (x+y)(x–y)=x2-xy+xy-y2

x2-y2

Squaring binomial (x+y)(x+y)=(x+y)2

=x2+2xy+y2

Conjugates (x+y)(x–y)=x2-xy+xy-y2

x2-y2

Treat complex numbers like binomials, ¡que facil!

Treat complex numbers like binomials, ¡que facil!

(3-6i)*2i =3*2i–6i*2i =6i-12i2

=12+6i You need to remember to simplify the i and

combine like terms!

(3-6i)*2i =3*2i–6i*2i =6i-12i2

=12+6i You need to remember to simplify the i and

combine like terms!

ExamplesExamples