How can I convert the complex number i^{\pi} to trigonometric

jelentetvq

jelentetvq

Answered question

2022-01-27

How can I convert the complex number iπ to trigonometric form?
I usually do these steps:
1. take Z=a+bi form,
2. find r=a2+b2
3. cos(ϕ)=ar, sin(ϕ)=br
4. find ϕ from the above 2 equations.

Answer & Explanation

chaloideq1

chaloideq1

Beginner2022-01-28Added 11 answers

ComplexExpand
[iπ]
cos(π22)+isin(π22)
π22 from i=eiπ2
Amari Larsen

Amari Larsen

Beginner2022-01-29Added 10 answers

Some useful identities:
i=eiπ2
(ab)c=a(bc)
eiϕ=cosϕ+isinϕ
Your expression:
iπ=(eiπ2)π=eiπ22=1(cos(π22)+isin(π22))

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