Question

(3(cos π\3 + i sin π\3))²

Answer 1

Ответ: 9*(0,5+i*0,5*корень из 3)^2=9*(0,25+i*0,5*корень из 3-0,75)=9*(-0,5+0,5*i*корень из 3)=-4,5+4,5*i*корень из 3.

Пошаговое объяснение:

Answer 2

To calculate the expression (3(cos π/3 + i sin π/3))^2, we first need to simplify the expression inside the parentheses, then square it. Let's break it down step by step:

Step 1: Simplify the expression inside the parentheses. Using Euler's formula, we know that cos(π/3) + i sin(π/3) = e^(iπ/3). Therefore, the expression inside the parentheses becomes:

3(e^(iπ/3)).

Step 2: Square the simplified expression. To square the expression, we multiply it by itself:

(3(e^(iπ/3)))^2 = 3^2 * (e^(iπ/3))^2 = 9 * e^(2iπ/3).

Step 3: Simplify further (if needed). Using Euler's formula again, we know that e^(iπ) = cos(π) + i sin(π) = -1. Therefore, e^(2iπ) = (e^(iπ))^2 = (-1)^2 = 1.

Now, e^(2iπ/3) = e^(2iπ) * e^(iπ/3) = 1 * e^(iπ/3) = e^(iπ/3) = cos(π/3) + i sin(π/3).

Step 4: Final result. Putting it all together, we have:

(3(cos π/3 + i sin π/3))^2 = 9 * (cos π/3 + i sin π/3) = 9 * cos(π/3) + 9i * sin(π/3).

So, the final result is 9 * cos(π/3) + 9i * sin(π/3).