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

$$findthevalueof...$$$$1-\frac{1}{1+\frac{1}{\frac{i}{1+\frac{i}{1+i}}}}$$$$plshelp.$$

Answered by ajfour last updated on 01/Jan/19

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

Commented by aseerimad last updated on 01/Jan/19

Thank you!

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