If \( i z^{4}+1=0 \), where \( i=\sqrt{-1} \), then \( z \) can take the value (a) \( \frac{1+i}...

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If \( i z^{4}+1=0 \), where \( i=\sqrt{-1} \), then \( z \) can take the value
(a) \( \frac{1+i}{\sqrt{2}} \)
(b) \( \cos \left(\frac{\pi}{8}\right)+i \sin \left(\frac{\pi}{8}\right) \)
(c) \( \frac{1}{4 i} \)
(d) \( i \)
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