What is ((1+i)^2)/(2+i) ?

The solution to ((1+i)^2)/(2+i) is 2/5+4/5 i

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simplify ((1+i)^2)/(2+i)

simplify

\frac{( 1 + i ) ^{2}}{2 + i}

\frac{2}{5} + \frac{4}{5} i

Solution steps

\frac{( 1 + i ) ^{2}}{2 + i}

Multiply by the conjugate

\frac{2 - i}{2 - i}

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

Simplify

\frac{( 1 + i ) ^{2} ( 2 - i )}{( 2 + i ) ( 2 - i )} : \frac{4 i + 2}{5}

= \frac{4 i + 2}{5}

Rewrite in standard complex form:

\frac{2}{5} + \frac{4}{5} i

= \frac{2}{5} + \frac{4}{5} i

y \cdot y

- 3 (x + 4) + 4

\frac{x ^{2} - 5 x - 6}{x ^{2} - 1}

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

\frac{5}{3} + 5