# rationals & the number i

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Category: Education

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### RATIONALS AND :

RATIONALS AND By: Mike And Sam

### i :

i i= i i2 = -1 i3 = -i (i x i2) i4 = 1 (i2 x i2)

### Multiplying by i :

Multiplying by i (3+2i) (3-2i) = 9-6i+6i-4i2 Notice how the 6’s will cancel You are left with 9-4i2 Notice however, that i2=-1. So you are really left with 9-(4(-1)), or 9+4 The answer to this problem is, 13.

### Dividing by i :

Dividing by i Make sure to multiply by the conjugate!!! 3+2i conjugate = 3-2i -4+5i conjugate = -4-5i The conjugate of 3-2i, is 3+2i, so therefore multiply both the top and bottom by 3+2i 5(3+2i) (3-2i)3+2i) You get 15+10i 9-4i2 which equals 13

### Rational Expressions :

Rational Expressions Division: a/b, making sure that b doesn’t equal 0. X2-9= (x+3)(x-3) X2+2x-15= (x+5)(x-3) The x-3’s will cancel so you are left with (x+3) (x+5) So x, can not equal -5

### Multiplying Rationals :

Multiplying Rationals X = X = =