vereinfachen (cos(θ)+isin(θ))^2(1+2cos(θ))

Lösung

vereinfachen

(cos (θ) + i sin (θ))^{2} (1 + 2 cos (θ))

(cos (2 θ) + 2 cos (2 θ) cos (θ)) + (sin (2 θ) + 2 cos (θ) sin (2 θ)) i

Schritte zur Lösung

(cos (θ) + i sin (θ))^{2} (1 + 2 cos (θ))

Schreibe

(cos (θ) + i sin (θ))^{2}

um:

i sin (2 θ) + cos (2 θ)

= (i sin (2 θ) + cos (2 θ)) (1 + 2 cos (θ))

Apply FOIL method

(i sin (2 θ) + cos (2 θ)) (1 + 2 cos (θ)) : sin (2 θ) i + 2 cos (θ) sin (2 θ) i + cos (2 θ) + 2 cos (2 θ) cos (θ)

= sin (2 θ) i + 2 cos (θ) sin (2 θ) i + cos (2 θ) + 2 cos (2 θ) cos (θ)

Rewrite in standard complex form:

(cos (2 θ) + 2 cos (2 θ) cos (θ)) + (sin (2 θ) + 2 cos (θ) sin (2 θ)) i

= (cos (2 θ) + 2 cos (2 θ) cos (θ)) + (sin (2 θ) + 2 cos (θ) sin (2 θ)) i

e x p an d (3 x - 5 y = 4,) (3 x - 2 y = 12)

s im pl i f y \frac{x + y i - 3}{( x + y i ) ^{2} + 2 ( x + y i ) + 2}

e x p an d \frac{1}{s ( s ^{3} + 6 s ^{2} + 11 x + 6 )}

e x p an d - e^{3 x} (e^{- x} + 1)

e x p an d (1 + 2 π sin (2 π t))^{2}