What is (1+i)/(sqrt(3)+i) ?

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

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simplify (1+i)/(sqrt(3)+i)

simplify

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

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

Solution steps

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

Multiply by the conjugate

\frac{3 - i}{3 - i}

= \frac{( 1 + i ) ( 3 - i )}{( 3 + i ) ( 3 - i )}

Simplify

\frac{( 1 + i ) ( 3 - i )}{( 3 + i ) ( 3 - i )} : \frac{3 + 1 + ( - 1 + 3 ) i}{4}

= \frac{3 + 1 + ( - 1 + 3 ) i}{4}

Rewrite in standard complex form:

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

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

\frac{1}{12} \cdot 2

(x^{3} + 6 x^{2} - 4 x + 7) - (3 x^{2} + 2 x - 4)

(3 i)^{2}

3 (x - 1) (x + 2)

\frac{1}{8} \cdot \frac{4}{5}

What is (1+i)/(sqrt(3)+i) ?
The solution to (1+i)/(sqrt(3)+i) is (sqrt(3)+1)/4+(-1+sqrt(3))/4 i