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  • If <img alt="\left ( \frac{1+i}{1-i} \right )^{\frac{m}{2}}=\left ( \frac{1+i}{1-i} \right )^{\frac{n}{3}}=1, (m, n\epsilon N)" src="http://entrancecorner.codecogs.com/gif.latex?%5Cleft%20%28%20%5Cfrac%7B1&plus;i%7D%7B1-i%7D%20%5Cright%20%29%5

If \left ( \frac{1+i}{1-i} \right )^{\frac{m}{2}}=\left ( \frac{1+i}{1-i} \right )^{\frac{n}{3}}=1, (m, n\epsilon N) then the greatest common divisior of the least values of m and n is________
Option: 1 4
Option: 2 2
Option: 3 3
Option: 4 5

Answers (1)

best_answer

\left ( \frac{1+i}{1-i} \right )^{\frac{m}{2}}=\left ( \frac{1+i}{1-i} \right )^{\frac{n}{3}}=1

\left ( \frac{1+i}{1-i}\times \frac{-1-i}{-1-i} \right )^{\frac{m}{2}}

=(i)^{\frac{m}{2}}

\frac{m}{2}=4\Rightarrow m=8

\left ( \frac{1+i}{1-i}\times \frac{-1-i}{-1-i} \right )^{\frac{n}{3}}

=(-i)^{\frac{n}{3}}

\frac{n}{3}=4\Rightarrow n=12

\therefore GCD=4

Posted by

Suraj Bhandari

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