What is (1+i)/i-3/(4-i) ?

The solution to (1+i)/i-3/(4-i) is 5/17-20/17 i

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simplify (1+i)/i-3/(4-i)

simplify

\frac{1 + i}{i} - \frac{3}{4 - i}

\frac{5}{17} - \frac{20}{17} i

Solution steps

\frac{1 + i}{i} - \frac{3}{4 - i}

\frac{1 + i}{i} = - i + 1

\frac{3}{4 - i} = \frac{12 + 3 i}{17}

= - i + 1 - \frac{12 + 3 i}{17}

Join

- i + 1 - \frac{12 + 3 i}{17} : \frac{- 20 i + 5}{17}

= \frac{- 20 i + 5}{17}

Rewrite in standard complex form:

\frac{5}{17} - \frac{20}{17} i

= \frac{5}{17} - \frac{20}{17} i

\frac{7}{4 - 9 i}

z^{2} - 6 z + 9 = - 4

- 4 x^{2} + 36

x^{3} - x^{2} + x + 3

\frac{2}{7} (\frac{665}{666}) + \frac{1}{9} = \frac{12}{5} (\frac{668}{666}) - \frac{14}{7}