KCET · Maths · Complex Number
The imaginary part of \(i^{i}\) is
- A 0
- B 1
- C 2
- D -1
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
Let \((a+i b)=i^{i}\)
Taking log on both sides, we get
\(\log (a+i b)=i \log i\)
\(\Rightarrow \quad \log (a+i b)=i(i \pi / 2)\)
\(\Rightarrow \quad \log (a+i b)=-\frac{\pi}{2}\)
\(\Rightarrow \quad(a+i b)=e^{-\pi / 2}\)
On comparing imaginary part of \(i^{i}\) is 0 .
Taking log on both sides, we get
\(\log (a+i b)=i \log i\)
\(\Rightarrow \quad \log (a+i b)=i(i \pi / 2)\)
\(\Rightarrow \quad \log (a+i b)=-\frac{\pi}{2}\)
\(\Rightarrow \quad(a+i b)=e^{-\pi / 2}\)
On comparing imaginary part of \(i^{i}\) is 0 .
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