Find-the-least-positive-integer-n-such-that-2i-1-i-n-is-a-ve-integer-

Question Number 49169 by rahul 19 last updated on 04/Dec/18

F i n d t h e l e a s t p o s i t i v e i n t e g e r n s u c h

t h a t {(\frac{2 i}{1 + i})}^{n} i s a + v e i n t e g e r ?

Answered by tanmay.chaudhury50@gmail.com last updated on 04/Dec/18

{(\frac{2 i (1 - i)}{2})}^{n}

= {(i + 1)}^{n} f o r n = 2 k

= {(1 + 2 i - 1)}^{k} = {(2 i)}^{k} [k = 2 p

= {(2 i)}^{2 p} = {(- 4)}^{p}

f o r p = 2 {(- 4)}^{2} = 16

s o n = 2 \times (2 \times 2) = 8

s o n = 8

Commented by rahul 19 last updated on 04/Dec/18

thanks sir ��