If \text{ }\big(x-\frac{1}x\big)=i\sqrt{2}. Then compute (x^{2187}-\frac{1}{x^{2187}}). Here i=\sqrt{-1}

estrigaslju

estrigaslju

Answered question

2022-04-20

If    (x1x)=i2. Then compute (x21871x2187).
Here i=1

Answer & Explanation

Savanah Wilkerson

Savanah Wilkerson

Beginner2022-04-21Added 13 answers

2187=37. This is a clue. Powers of 3 are significant. Now
(x1x)3=(i2)3=2i2
and (x1x)3=x31x33(x1x)=x31x33i2.
So x31x3=i2.
Repeating this, x91x9=i2,
x271x27=i2
etc. Eventually, x21871x2187=i2.

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