Question

prove that 1+i²+i⁴+i⁶=0​

Answer 1

$\huge\boxed{\fcolorbox{purple}{ink}{Answer}}$

$= 1 + {i}^{2} + {i}^{4} + {i}^{6} \\ \\ = 1 + (- 1) + (1) + (i) {}^{2} . {i}^{4} \\ \\ = 1 - 1 + 1 - 1 \\ \\ = 0$

Answer 2

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$\sf\underline\red{Proving:}$

$\begin{gathered}= 1 + {i}^{2} + {i}^{4} + {i}^{6} \\ \\ = 1 + (- 1) + (1) + (i) {}^{2} . {i}^{4} \\ \\ = 1 - 1 + 1 - 1 \\ \\ = 0\end{gathered}$