express 2(cos 4pi/3 + i sin 4pi/3) in the form x+iy
2[-0.5 +(-i 0.866)]
looks good to me, though you should probably expand it out to the desired form.
-1 - √3 i
To express the given complex number in the form x + iy, we need to simplify it using Euler's formula. Euler's formula states that e^(iθ) = cos(θ) + i sin(θ), where i is the imaginary unit.
Let's simplify the expression step by step:
First, let's rewrite the given number using Euler's formula:
cos(4π/3) + i sin(4π/3)
Using Euler's formula, this becomes:
e^(i(4π/3))
Now, we can rewrite e^(i(4π/3)) using the complex exponential form:
e^(iθ) = cos(θ) + i sin(θ)
θ = 4π/3
So, e^(i(4π/3)) = cos(4π/3) + i sin(4π/3)
Therefore, we can express the given complex number in the form x + iy as:
2(cos(4π/3) + i sin(4π/3))
Thus, the final expression is:
2cos(4π/3) + 2i sin(4π/3)