What is 1+i/(1+\frac{i){1+i/(1+i)}} ?

The solution to 1+i/(1+\frac{i){1+i/(1+i)}} is 4/3+2/3 i

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simplify 1+i/(1+\frac{i){1+i/(1+i)}}

simplify

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

\frac{4}{3} + \frac{2}{3} i

Solution steps

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

Simplify

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

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

Join

1 + \frac{1 + 2 i}{3} : \frac{4 + 2 i}{3}

= \frac{4 + 2 i}{3}

Rewrite in standard complex form:

\frac{4}{3} + \frac{2}{3} i

= \frac{4}{3} + \frac{2}{3} i

tan (θ) cos (θ)

\frac{6}{8} \cdot \frac{3}{5}

sin^{2} (2 t) + cos^{2} (2 t)

2^{2 - 4}

What is 1+i/(1+\frac{i){1+i/(1+i)}} ?
The solution to 1+i/(1+\frac{i){1+i/(1+i)}} is 4/3+2/3 i