Paano mo multiply e ^ ((2 pi) / 3 i) * e ^ (pi / 2 i) sa trigonometriko form?

Sagot:

#cos ((7pi) / 6) + isinisi (7pi) / 6) = e ^ ((7pi) / 6i) #

Paliwanag:

# e ^ (itheta) = cos (theta) + isin (theta) #

# e ^ (itheta_1) * e ^ (itheta_2) == cos (theta_1 + theta_2) + isin (theta_1 + theta_2) #

# theta_1 + theta_2 = (2pi) / 3 + pi / 2 = (7pi) / 6 #

#cos ((7pi) / 6) + isinisi (7pi) / 6) = e ^ ((7pi) / 6i) #

Sagot:

Ang sagot ay # == - sqrt3 / 2 + 1 / 2i #

Paliwanag:

Ang isa pang paraan.

# i ^ 2 = -1 #

Kaugnayan ni Euler

# e ^ (itheta) = costheta + isintheta #

Samakatuwid, # e ^ (2 / 3pii) * e ^ (pi / 2i) = (cos (2 / 3pi) + isinisin (2 / 3pi)) (cos (pi / 2)

# = (1/2 + isqrt3 / 2) (0 + i) #

# = 1 / 2i-sqrt3 / 2 #

# = - sqrt3 / 2 + 1 / 2i #