\[{\imath }^{99}\]
1
Use Power Reduction Rule: in=in mod 4{i}^{n}={i}^{n\text{ mod }4}.
ı3{\imath }^{3}

2
Isolate ı2{\imath }^{2}.
ı2ı{\imath }^{2}\imath

3
Use Square Rule: i2=−1{i}^{2}=-1.
−1×ı-1\times \imath

4
Simplify.
−ı-\imath

Done
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