Question

(i^18+(1/i )^25)^3=2(1-i)

Answer 1

plz see attached image
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Answer 2

Answer:

$\longrightarrow\tt{\bigg[{i}^{18}+\bigg(\dfrac{1}{i}\bigg)^{25}\bigg]^{3}}$

$\longrightarrow\tt\bigg[{i}^{4\times4+2}+\dfrac{1}{{i}^{4\times6+1}}\bigg]^{3}$

$\longrightarrow\tt{\bigg(-1+\dfrac{1}{i}\bigg)^{3}}$

$\longrightarrow\tt{(-1)^3+\bigg(\dfrac{1}{i}\bigg)^3+3(-1)\bigg(\dfrac{1}{i}\bigg)\bigg(-1+\dfrac{1}{i}\bigg)}$

$\longrightarrow\tt{-1+\dfrac{1}{-i}+\bigg(\dfrac{-3}{i}\bigg)\bigg(\dfrac{-1i+1}{i}\bigg)}$

$\longrightarrow\tt{-1-\dfrac{-1}{i}-\dfrac{3}{i}\bigg(\dfrac{-1i+1}{i}\bigg)}$

$\longrightarrow\tt{-1-\dfrac{1}{i}+\dfrac{3i-3}{i^{2}}}$

$\longrightarrow\tt{-1-\dfrac{1}{i}+\bigg(\dfrac{-3i+3}{1}\bigg)}$

$\longrightarrow\tt{-1-\dfrac{1}{i}-3i+3}$

$\longrightarrow\tt{\dfrac{-1-3i^{2}}{i}+2}$

$\longrightarrow\tt{\dfrac{-1+3}{i}+2}$

$\longrightarrow\tt{\dfrac{-1+3+2i}{i}}$

$\longrightarrow\tt{\dfrac{2+2i}{i}\times\dfrac{i}{i}}$

$\longrightarrow\tt{\dfrac{2i+2i^{2}}{-1}}$

$\longrightarrow\tt{\dfrac{2i+(-2)}{-1}}$

$\longrightarrow\tt{-(2i-2)}$

$\longrightarrow\bf\underline{2(1-i)}$