Let&nbsp;\(\alpha &gt; \beta \in \mathbb{R}\). Prove that
\[e^{i\alpha} + e^{i\beta} = 2 \cos \left( \frac{\alpha - \beta}{2} \right) e^{i \left( \frac{\alpha + \beta}{2} \right)}.\]
[Hint: There are \(3\) ways to prove this.]

Let \(\alpha > \beta \in \mathbb{R}\). Prove that

\[e^{i\alpha} + e^{i\beta} = 2 \cos \left( \frac{\alpha - \beta}{2} \right) e^{i \left( \frac{\alpha + \beta}{2} \right)}.\]

[Hint: There are \(3\) ways to prove this.]

Special Results involving Exponential Forms [Out of Syllabus]

Complex Numbers

International Baccalaureate Higher Level Mathematics

Vector sum of complex numbers via exponential representation

Vector sum of complex numbers via exponential representation