What is (3+isqrt(3))/(3-isqrt(3)) ?

The solution to (3+isqrt(3))/(3-isqrt(3)) is 1/2+(sqrt(3))/2 i

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simplify (3+isqrt(3))/(3-isqrt(3))

simplify

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

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

Solution steps

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

Rewrite

3 + i 3

in standard complex form:

3 + 3 i

Rewrite

3 - i 3

in standard complex form:

3 - 3 i

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

Multiply by the conjugate

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

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

Simplify

\frac{( 3 + 3 i ) ( 3 + 3 i )}{( 3 - 3 i ) ( 3 + 3 i )} : \frac{6 3 i + 6}{12}

= \frac{6 3 i + 6}{12}

Rewrite in standard complex form:

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

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

- 1 \leq \frac{2 x - 3}{2} < 4

- 21 x - 6 x^{2}

- 3 ∣ x + 9 ∣ + 2 = 10 ∣ x + 9 ∣ + 5

\frac{- 4 - 5}{8 - 2}

0 = x^{2} - 16 x + 48

What is (3+isqrt(3))/(3-isqrt(3)) ?
The solution to (3+isqrt(3))/(3-isqrt(3)) is 1/2+(sqrt(3))/2 i