Convert 2e^((pi*i)/6) to rectangular form
To convert a complex number from exponential form to rectangular form, you can use Euler's formula:
e^(ix) = cos(x) + i*sin(x)
In this case, the given number is 2e^((pi*i)/6). Let's break it down:
1. Rewrite the exponential form using Euler's formula:
2e^((pi*i)/6) = 2 * (cos((pi*i)/6) + i*sin((pi*i)/6))
2. Simplify the trigonometric functions:
cos((pi*i)/6) = cos(pi/6) = sqrt(3)/2
sin((pi*i)/6) = sin(pi/6) = 1/2
3. Substitute the values back into the equation:
2 * (sqrt(3)/2 + i*(1/2))
4. Simplify the expression:
2 * sqrt(3)/2 + 2 * i * (1/2) = sqrt(3) + i
So, the rectangular form of the complex number 2e^((pi*i)/6) is sqrt(3) + i.
Recall that e^(iθ) = cosθ + i sinθ
so, 2e^(i π/6) = 2(cos(π/6) + i sin(π/6))
now just finish up the details