Question

Write 5(cos(5π/3) + i sin(5π/3)) in exponential form.

Answer 1

To write 5(cos(5π/3) + i sin(5π/3)) in exponential form, we can use Euler's formula: e^(iθ) = cos(θ) + i sin(θ).

Step-by-step explanation:

To write 5(cos(5π/3) + i sin(5π/3)) in exponential form, we can use Euler's formula: e^(iθ) = cos(θ) + i sin(θ). In this case, θ = 5π/3. So, we have:

5(cos(5π/3) + i sin(5π/3)) = 5e^(i(5π/3))

Using the formula e^(iθ) = cos(θ) + i sin(θ), we can rewrite it as:

5e^(i(5π/3)) = 5e^((5π/3)i)