What is (7+sqrt(-3))/(1+sqrt(-12)) ?

The solution to (7+sqrt(-3))/(1+sqrt(-12)) is 1-sqrt(3)i

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simplify (7+sqrt(-3))/(1+sqrt(-12))

simplify

\frac{7 + - 3}{1 + - 12}

1 - 3 i

Solution steps

\frac{7 + - 3}{1 + - 12}

Multiply by the conjugate

\frac{1 - - 12}{1 - - 12}

= \frac{( 7 + - 3 ) ( 1 - - 12 )}{( 1 + - 12 ) ( 1 - - 12 )}

Expand

(7 + - 3) (1 - - 12) : - 133 i + 13

Expand

(1 + - 12) (1 - - 12) : 13

= \frac{- 13 3 i + 13}{13}

Factor out common term

13 : 13 (- 3 i + 1)

= \frac{13 ( - 3 i + 1 )}{13}

Rewrite in standard complex form:

1 - 3 i

= 1 - 3 i

12 - 6 x

\frac{25 x ^{5} y ^{2}}{x ^{8} y ^{3}}

(3 x - 4 y)^{4}

\frac{9 x}{8} + \frac{7}{3}

- x^{2} - 4 x - 1

What is (7+sqrt(-3))/(1+sqrt(-12)) ?
The solution to (7+sqrt(-3))/(1+sqrt(-12)) is 1-sqrt(3)i