Final answer:
The complex number e⁶²π/³ is written in standard form as -1/2 + i(√3/2), with a = -1/2 and b = √3/2.
Step-by-step explanation:
The complex number e⁶²π/³ can be written in the form a+bi by using Euler's formula, which states eiθ = cos(θ) + i sin (θ). For θ = 2π/3, we find the cos(2π/3) = -1/2 and sin(2π/3) = √3/2. Therefore, the complex number in the form a+bi is -1/2 + i(√3/2).
Rephrasing the original question: Write the complex number e²π/³ in the form a+bi. The solution is a = -1/2 and b = √3/2.