Using Euler's formula e^{i θ} = cos θ + i sin θ, evaluate e^{iπ}.

• A. e^{iπ} = -1
• B. e^{iπ} = 1
• C. e^{iπ} = i
• D. e^{iπ} = -i

Answer: (A)

Using Euler's formula, plug in θ = π: e^{iπ} = cos π + i sin π. We know cos π = -1 and sin π = 0, so e^{iπ} = -1 + 0i = -1. Geometrically, the angle π points to the left on the unit circle, at the real value -1. So the value is -1.