Question

simplify i^65+1÷i^145​

Answer 1

Answer:-

$\sf{\frac{i^{65}}{i^{145}}=1}$

Solution:

$\sf{\implies{\frac{i^{65}}{i^{145}}}}$

$\sf{=\frac{(i^{4})^{21}.i}{(i^{4})^{36}.i}}$

$\sf{=\frac{i}{i}...[\because{i^{4}=1}]}$

$\sf{=1}$

$\sf\purple{\tt{\therefore{\frac{i^{65}}{i^{145}}=1}}}$

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$\sf\blue{\underline{\underline{Extra \ information}}}$

$\sf{i=\sqrt{-1}}$

$\sf{i^{2}=-1}$

$\sf{i^{3}=-i}$

$\sf{i^{4}=1}$