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Rational Expressions Worksheet

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Mathematics

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1. Factor x
2
+ 64. Check your work.
= (x - 8i) (x + 8i)
x^2 + 8ix - 8ix - 64i^2
x^2 + 64
2. Factor 16x
2
+ 49. Check your work.
= (4x - 7i) (4x + 7i)
16x^2 + 28ix - 28ix - 49i^2
16x^2 - 49i^2
16x^2 + 49
3. Find the product of (x + 9i)
2
.
= (x + 9i) (x + 9i)
x^2 + 9ix + 9ix + 81i^2
x^2 + 18ix + 81(-1)
x^2 + 18ix - 81
4. Find the product of (x − 2i)
2
.
= (x - 2i) (x - 2i)
x^2 - 2ix - 2ix + 4i^2
x^2 - 4ix + 4(-1)
x^2 - 4ix - 4
5. Find the product of (x + (3+5i))
2
.
=(x + (3 + 5i))(x + (3+5i))
x^2 + x(3+5i) + x(3+5i) + (3 + 5i)^2
x^2 + 2x(3+5i) + 9 + 6(5i) + 25i^2
x^2 + 6x +10xi + 9 + 30i - 25
x^2 + 6x + 10xi + 30i - 16
Essential Question:
How do polynomial identities apply to complex numbers?
Each piece of the polynomial identity applies to complex numbers such as (x+bi)^2=x^2+2(x*bi)+(bi)^2

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1. Factor x2 + 64. Check your work. = (x - 8i) (x + 8i) x^2 + 8ix - 8ix - 64i^2 x^2 + 64 2. Factor 16x2 + 49. Check your work. = (4x - 7i) (4x + 7i) 16x^2 + 28ix - 28ix - 49i^2 16x^2 - 49i^2 16x^2 + 49 3. Find the product of (x + 9i)2. = (x + 9i) (x + 9i) x^2 + 9ix + 9ix + 81i^2 x^2 + 18ix + 81(-1) ...
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