Question

4 Не виконуючи обчислень, порівняйте: 1) різнищо чисел -6,81 i —12,97 та їх суму;2) різницю чисел 31 i —72 та різницю чисел -96 i — 62.Відповідь обгрунтуйте.​

Answer 1

Ответ:

1.-6,81-12,97=-19,78 2. 31-72 (-96-62)=-41-96-62=-199

Answer 2

Comparison of Complex Numbers

To compare the given complex numbers without performing calculations, let's analyze the real and imaginary parts separately.

1) Difference of -6.81i and -12.97i and their sum:

The real part of both numbers is 0, so the sum of the real parts will also be 0.

The imaginary part of -6.81i is -6.81, and the imaginary part of -12.97i is -12.97. Since both numbers have negative imaginary parts, we can conclude that the sum of these numbers will have a negative imaginary part as well.

Therefore, the sum of -6.81i and -12.97i will have a real part of 0 and a negative imaginary part.

2) Difference of 31i and -72i and the difference of -96i and 62i:

The real part of both numbers is 0, so the difference of the real parts will also be 0.

The imaginary part of 31i is 31, and the imaginary part of -72i is -72. Since one number has a positive imaginary part and the other has a negative imaginary part, we can conclude that the difference of these numbers will have a positive imaginary part.

Similarly, the imaginary part of -96i is -96, and the imaginary part of 62i is 62. Since one number has a negative imaginary part and the other has a positive imaginary part, we can conclude that the difference of these numbers will have a negative imaginary part.

Therefore, the difference of 31i and -72i will have a real part of 0 and a positive imaginary part, while the difference of -96i and 62i will have a real part of 0 and a negative imaginary part.

In summary: 1) The sum of -6.81i and -12.97i will have a real part of 0 and a negative imaginary part. 2) The difference of 31i and -72i will have a real part of 0 and a positive imaginary part. 3) The difference of -96i and 62i will have a real part of 0 and a negative imaginary part.

Please note that the provided search results did not directly answer the question. However, the comparison of complex numbers can be done by analyzing their real and imaginary parts, as explained above.