Question

find value of this picture attached​

Answer 1

Solution:

$\sf{\leadsto{[i^{17}+\dfrac{1}{i^{315}}]^{9}}}$

$\sf{\leadsto{[(i^{4})^{4}.i+\dfrac{1}{(i^{4})^{78}.i^{3}}]^{9}}}$

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

$\sf{\leadsto{[1^{4}.i+\dfrac{1}{1^{78}.i^{3}}]^{9}}}$

$\sf{\leadsto{[i+\dfrac{1}{i^{3}}]^{9}}}$

$\sf{\leadsto{(i+i)^{9}}}$

$\sf{\leadsto{(2i)^{9}}}$

$\sf{\leadsto{512(i^4)^{2}.i}}$

$\sf\purple{\tt{\leadsto{512i}}}$

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Extra information:

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

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

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

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