What is ((3+6i)^2)/(2i) ?

The solution to ((3+6i)^2)/(2i) is 18+27/2 i

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simplify ((3+6i)^2)/(2i)

simplify

\frac{( 3 + 6 i ) ^{2}}{2 i}

18 + \frac{27}{2} i

Solution steps

\frac{( 3 + 6 i ) ^{2}}{2 i}

Multiply by the conjugate

\frac{- i}{- i}

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

Simplify

\frac{( 3 + 6 i ) ^{2} ( - i )}{2 i ( - i )} : \frac{36 + 27 i}{2}

= \frac{36 + 27 i}{2}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{36}{2} + \frac{27}{2} i

Divide the numbers:

\frac{36}{2} = 18

= 18 + \frac{27}{2} i

\frac{a ^{4} + a}{a + 1}

cot^{2} (x) sec^{2} (x)

\frac{\frac{4 y - 16}{5 y + 15}}{\frac{4 - y}{2 y + 6}}