If z - i i-where i -1- then Re z isA- ZeroB- None of theseC- e - - 2D- e -

The correct option is C z = i^i = (e^iπ/2)^i = e^ π/2 ⇒ Re(z) = e^ π/2 ...

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Square Root of a Complex Number

If z = i i,wh...

Question

If $z = i^{i}$ ,where i = $\sqrt{- 1}$ , then Re(z) is

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zero

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None of these

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If $z = (i)^{i}$ , where $i = \sqrt{- 1}$ , then Re(z) is:

z = (1 - i)^{- i}

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\pm \frac{π}{4}, \pm \frac{3 π}{4}

\sqrt{- 1} = i

\sqrt{z} = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \sqrt{\frac{| z | + R e (z)}{2}} + i \sqrt{\frac{| z | - R e (z)}{2}} & , if B > 0 \sqrt{\frac{| z | + R e (z)}{2} - i \sqrt{\frac{| z | - R e (z)}{2}}} & , if B < 0 \end{matrix}

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