Ψιρψθσ / Διαγοναλ Ψιρψθμφ ρεφερενψε / Διαμετερ Applications in complex number theory [ edit ] Euler's formula e iφ = cos φ + i sin φ illustrated in the complex plane. Interpretation of the formula [ edit ] This formula can be interpreted as saying that the function e iφ is a unit complex number , i.e., it traces out the unit circle in the complex plane as φ ranges through the real numbers. Here φ is the angle that a line connecting the origin with a point on the unit circle makes with the positive real axis , measured counterclockwise and in radians . Any complex number can be written as z = x + iy , Σ = ψοσ(φ) + γ(φ) and its complex conjugate, z = x − iy , can be written as {\displaystyle {\begin{aligned}z&=x+iy=|z|(\cos \varphi +i\sin \varphi )=re^{i\varphi },\...