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

The solution to ((2+i)^2(-i))/(1+i) is 1/2-7/2 i

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

simplify

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

\frac{1}{2} - \frac{7}{2} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 2 + i ) ^{2} ( - i ) ( 1 - i )}{( 1 + i ) ( 1 - i )} : \frac{1 - 7 i}{2}

= \frac{1 - 7 i}{2}

Rewrite in standard complex form:

\frac{1}{2} - \frac{7}{2} i

= \frac{1}{2} - \frac{7}{2} i

\frac{1}{5 ^{- 5}}

\frac{13}{5} \div \frac{5}{10}

(9 + x - 3) (9 + x + 3)

(1 + 0.1)^{2}

4 - 12