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For any number n>1, is

(0.7 + 0.7i)n

a. Greater than 1?

b. Less than 1?

C. Equal to 1?


Sagot :

Using complex numbers, it is found that the correct option regarding the expression is:

a. Greater than 1.

What are complex numbers?

Complex numbers are numbers that have a real and an imaginary part, and are modeled by:

[tex]z = a + bi[/tex]

In which:

  • a is the real part.
  • b is the imaginary part.

The magnitude of the number is:

[tex]|z| = \sqrt{a^2 + b^2}[/tex]

In this problem, the number is:

[tex](0.7 + 0.7i)n[/tex]

The smallest possible value is n = 4, hence:

[tex]z = 1.4 + 1.4i[/tex]

And the magnitude is:

[tex]\sqrt{1.4^2 + 1.4^2} = 1.98[/tex]

Which is greater than 1, hence option a is correct.

You can learn more about complex numbers at https://brainly.com/question/25572463

Answer: it’s b

Step-by-step explanation: the answer is .98 which is less than 1