Q81 / 180 · KCET 2007 · Mathematics

The imaginary part of $i^{i}$ is

  • Correct answer
    A
    0
  • B
    1
  • C
    2
  • D
    -1

Solution

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 .

Hence, the correct answer is option: 'A'.

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