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If z^2 + 1 = 0, find z^(49) + z^(50) + z^(51) + z^(52).

 Oct 26, 2021
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We have \(z^{49}+z^{50}+z^{51}+z^{52}=z^{49}(1+z+z^2+z^3)\)

 

The term in parentheses factors as \(1+z+z^2+z^3=(z+1)(z^2+1)\)

 

So, if \(z^2+1=0\) then \(z^{49}+z^{50}+z^{51}+z^{52}=0\)

 Oct 26, 2021

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