Assignment:
Irrational, Real, and Complex Numbers
Q1. Classify the given numbers as real and rational, real and irrational, or complex.
- (4)1/2 + 2
- 6+0i
- 30007.413
- 3i
- 2-(-9)½ i
- (80)1/5
- 1
- (16)1/4
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Rational Number
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Irrational Number
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Complex Number
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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.
Q2. Using one of the laws of exponents, prove that any number raised to the power 0 is 1.
Q3. Using FOIL, simplify the expression "(3x + 2)(3x - 2)". Show that a particular factoring formula leads to the same answer.
Q4. 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.
Q5. 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.
(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.
Provide complete and step by step solution for the question and show calculations and use formulas.