What is 1/(1-2i)+3/(1+4i) ?

The solution to 1/(1-2i)+3/(1+4i) is 32/85-26/85 i

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simplify 1/(1-2i)+3/(1+4i)

simplify

\frac{1}{1 - 2 i} + \frac{3}{1 + 4 i}

\frac{32}{85} - \frac{26}{85} i

Solution steps

\frac{1}{1 - 2 i} + \frac{3}{1 + 4 i}

\frac{1}{1 - 2 i} = \frac{1 + 2 i}{5}

\frac{3}{1 + 4 i} = \frac{3 - 12 i}{17}

= \frac{1 + 2 i}{5} + \frac{3 - 12 i}{17}

Join

\frac{1 + 2 i}{5} + \frac{3 - 12 i}{17} : \frac{- 26 i + 32}{85}

= \frac{- 26 i + 32}{85}

Rewrite in standard complex form:

\frac{32}{85} - \frac{26}{85} i

= \frac{32}{85} - \frac{26}{85} i

4 \frac{3}{5} - 2 \frac{1}{3}

2 (5 - 4 y)

∣ 2 ∣ ∣ - 12 ∣

m^{2} - 121

\frac{1}{2.5 - 2}