Question

Найдите: $e^{i} , e ^{i pi } ,e ^{1+i}$

Answer 1

$e^{ialpha}:=cosalpha+isinalpha\ e^i=cos1+isin 1\ e^{ipi}=cospi+isinpi=-1\ e^{1+i}=e^1e^i=e(cos1+isin1)$

Answer 2

e^i = √(1/(1 + tg²1)) + i*tg1√(1/(1 + tg²1))
e^(πi) = -1
e^(1 + i) = e√(1/(1 + tg²1)) + i*e*tg1√(1/(1 + tg²1))