-i
Explanations:The given complex number is:
[tex]i^{15}[/tex]Note that:
[tex]i^2\text{ = -1}[/tex]Also note that:
[tex]\begin{gathered} i^{15}=i^{14}\times i^{\square} \\ i^{15}=(i^2)^7\times i \\ i^{15}=(-1)^7\times i \\ i^{15}=\text{ -1 }\times i \\ i^{15}=\text{ -i} \end{gathered}[/tex][tex]\text{The equivalence of i}^{15}=\text{ -i}[/tex]