 Ex. 8. Answer the following questions.

1. What were positive integers used for? 2. When was the number system completed? 3. Are the first numbers which we use the positive integers or the negative ones? 4. Is unity a first or a last integer? 5. By what is the division point between positive and negative numbers occupied? 6. What are rational numbers? 7. Can irrational numbers be expressed as quotients of two or three integers? 8. What numbers are called imaginaries? 9. What do we assign to each point on the line? 10. What do we use to denote the real part of a complex number?

Ex. 9. Find the Russian equivalents for the following English word combinations.

1. in either direction; 2. imaginaries; 3. is composed of; 4. real and imaginary parts; 5. a quotient of two integers; 6. the number system; 7. to denote the real part; 8. is replaced by; 9. the basic system; 10. in terms of; 11. to correspond to a subset.

a. основная система; b. система чисел; c. действительные и мнимые части; d. в любом направлении; e. заменяется; f. обозначать действительную часть; g. состоит из; h. мнимые числа; i. частное двух чисел; j. через, посредством; k. соответствовать подмножеству

Ex. 10. Give the proper English equivalents for the Russian expressions.

 Древность, соотношение, разделительная точка, делитель, рациональные и иррациональные числа, частное двух чисел, мнимые числа, запись, действительная и мнимая части.

1. … is occupied by the number zero. 2. The irrationals can not be expressed as …. 3. Positive fractions or numbers can be expressed as…of two of these integers. 4. We are not allowed to use the number zero as… 5. The beginning of our number system dates back to… 6. The real number system is formed of… 7. Numbers √-2, -√-1 are called… 8. The expression 2+√-3 is composed of… 9. To denote the real part of a complex number we use…

Ex. 11. Open the brackets putting the verbs in the correct form.

1. Why you (look at) me like that? 2. We (read) a book while he (cook) lunch at that time yesterday. 3. This time next month I (to cross) the Pacific Ocean. 4. I (wait) for you when you come out. 5. He (sit) in a cafй when I saw him. 6. I (go) to the cinema tonight. 7. Look! She (wear) the same dress as me. 8. Yesterday at 8 o’clock we (watch) the football match. 9. He (drive) his car himself today. 10. Great news! Jack (come) in a week.

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