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halk3431
@halk3431
June 2021
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Verified answer
Z =(i -1)/(i+1) =(-1+i)/(1+i) =√2
(
cos(π-π/4) +
i
sin(π-π/4)
)
/ √2
(
cosπ/4 +
i
sinπ/4
)
=
=cos(π-π/4 -π/4) +
i
sin(π-π/4-π/4) = cosπ/2 +
i
sinπ/2 .
алгебраическая форма z
= cosπ/2 +
i
sinπ/2
= 0+ i.
показательная форма я z =
cosπ/2 +
i
sinπ/2=
e^(i*π/2) .
-------------------------------
z =(-1+i)/(1+i) =(-1+i)(1-i)/(1+i)(1-i) =(-1+i +i -i²)/(1-i²) =(-1+i +i +1)/(1+1) =2i/2 =i.
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Answers & Comments
Verified answer
Z =(i -1)/(i+1) =(-1+i)/(1+i) =√2(cos(π-π/4) +isin(π-π/4)) / √2 (cosπ/4 +isinπ/4) ==cos(π-π/4 -π/4) +isin(π-π/4-π/4) = cosπ/2 +isinπ/2 .
алгебраическая форма z = cosπ/2 +isinπ/2 = 0+ i.
показательная форма я z =cosπ/2 +isinπ/2=e^(i*π/2) .
-------------------------------
z =(-1+i)/(1+i) =(-1+i)(1-i)/(1+i)(1-i) =(-1+i +i -i²)/(1-i²) =(-1+i +i +1)/(1+1) =2i/2 =i.