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    Algebra - Rational - Irrational Numbers

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    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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    https://brainmass.com/math/basic-algebra/algebra-rational-irrational-numbers-197427

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