find-the-value-of-1-1-1-1-i-1-i-1-i-pls-help-

Question Number 51922 by aseerimad last updated on 01/Jan/19

f i n d t h e v a l u e o f \dots

1 - \frac{1}{1 + \frac{1}{\frac{i}{1 + \frac{i}{1 + i}}}}

p l s h e l p .

Answered by ajfour last updated on 01/Jan/19

1 + \frac{i}{1 + i} = 1 + \frac{i (1 - i)}{2} = \frac{3 + i}{2}

1 + \frac{1}{\frac{i}{1 + \frac{i}{1 + i}}} = 1 + \frac{3 + i}{2 i} = \frac{3 + 3 i}{2 i}

1 - \frac{2 i}{3 + 3 i} = \frac{3 + i}{3 (1 + i)} = \frac{(3 + i) (1 - i)}{6}

= \frac{1 - i}{3} .

Commented by aseerimad last updated on 01/Jan/19

Thank you!