I hate to ask it…
How do we multiply and divide these
things?
Before 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
Multiplying binomials
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(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 cases
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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!
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(3-6i)*2i
=3*2i–6i*2i
=6i-12i2
=12+6i
You need to remember to simplify the i and
combine like terms!
Examples