What is (7i^2+10i)/(5i) ?

The solution to (7i^2+10i)/(5i) is 2+7/5 i

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simplify (7i^2+10i)/(5i)

simplify

\frac{7 i ^{2} + 10 i}{5 i}

2 + \frac{7}{5} i

Solution steps

\frac{7 i ^{2} + 10 i}{5 i}

Multiply by the conjugate

\frac{- i}{- i}

= \frac{( 7 i ^{2} + 10 i ) ( - i )}{5 i ( - i )}

Simplify

\frac{( 7 i ^{2} + 10 i ) ( - i )}{5 i ( - i )} : \frac{7 i + 10}{5}

= \frac{7 i + 10}{5}

Rewrite

7 i + 10

in standard complex form:

10 + 7 i

= \frac{10 + 7 i}{5}

Apply the fraction rule:

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

= \frac{10}{5} + \frac{7}{5} i

Divide the numbers:

\frac{10}{5} = 2

= 2 + \frac{7}{5} i

2 = (- \frac{2}{3}) (3) + b

\frac{5}{2 5 - 6}

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