If [tex]k\:\in\:N[/tex], then [tex]\frac{i^{4k+1}-i^{4k-1}}{2}[/tex] is equal to
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If [tex]k\:\in\:N[/tex], then [tex]\frac{i^{4k+1}-i^{4k-1}}{2}[/tex] is equal to
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Answer:
Step-by-step explanation:
Since,k belongs to natural numbers,we can substitute k=1,2,3,...
Take k=1.
i^(4k+1)=i
i^(4k-1)=-i
for k=1
So,
{i-(-i)}/2=2i/2=I
Hence, value of the given expression is i