How do we multiply and divide these things?

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Presentation transcript:

How do we multiply and divide these things? 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 (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 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! (3-6i)*2i =3*2i–6i*2i =6i-12i2 =12+6i You need to remember to simplify the i and combine like terms!

Examples