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

The solution to 3/(1+i)-4/(1-i) is -1/2-7/2 i

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

simplify

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

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

Solution steps

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

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

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

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

Join

\frac{3 - 3 i}{2} - \frac{4 + 4 i}{2} : \frac{3 - 3 i - ( 4 + 4 i )}{2}

= \frac{3 - 3 i - ( 4 + 4 i )}{2}

Simplify

3 - 3 i - (4 + 4 i) : - 7 i - 1

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

Rewrite in standard complex form:

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

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

(4 x^{- 2} y^{4})^{- \frac{1}{2}}

297

\frac{25 !}{7 ! ( 25 - 7 ) !}

3 a^{2} - 18 a + 27