Hallo,
( 5π)/12 =75°
verwende:
cos(α + β) = cos(α)·cos(β) – sin(α)·sin(β)
cos(30°+45°)= 1/4(√6-√2)
sin(α + β) = sin(α)·cos(β)+ cos(α)·sin(β)
sin(30°+45°)= 1/4(√2 +√6)
--->Euler Formel:
\( \mathrm{e}^{\mathrm{i} y}=\cos (y)+\mathrm{i} \sin (y) \)
-----> i *e^((5 π i)/12)= i (cos ((5 π i)/12) + i sin((5 π i)/12))
= -√2/4 -√6/4 +i (√6/4 -√2/4)
= -1/4 (√(2) + √(6)) +i 1/4 (√6-√2)
≈ \( -0.9659+0.2588 i \)
