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Algebra - Rational - Irrational Numbers

Assignment 1: Irrational, Real, and Complex Numbers

1. Classify the given numbers as real and rational, real and irrational, or complex.

a. (4)1/2 + 2
b. 6+0i
c. 30007.413
d. 3i
e. 2-(-9)_ i
f. (80)1/5
g. 1
h. (16)1/4

Rational Number Irrational Number Complex Number

2. a) Select any irrational number, and turn it into a rational number by using addition, subtraction, multiplication, division, or exponentiation.
b) Select any imaginary number (of the form "a + bi" where a and b are non-zero real numbers), and turn it into a real number by using addition, subtraction, multiplication, division, or exponentiation.

Assignment 2: Discussion Questions
1. Using one of the laws of exponents, prove that any number raised to the power 0 is 1.
2. Using FOIL, simplify the expression "(3x + 2)(3x - 2)". Show that a particular factoring formula leads to the same answer.
3. If a fourth-degree polynomial is multiplied by a third-degree polynomial, what is the degree of the product? Explain your reasoning and provide examples to support your explanation.
4. Think of a condition under which the product of any two binomials is a binomial. You can support your answer with the help of one of the identities of factorization of polynomials.
5. (i) Is "12.5555..." a rational or irrational number? Explain.
(ii) Is "2.1273685..." a rational or irrational number? Explain.
(iii) Is "548/799" a rational or irrational number? Explain.
(iv) Simplify "(5 + 3i)(5 - 3i)". Is the result real, complex, or both? Explain.

[See the attached questions file.]

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Neat and step-wise solutions are provided. Simplification and explanation is also provided.

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