What is (2 + square root of -3)(-1 + square root of -12)?

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Answer 1 · 2015-09-13T18:40:10

$- 8 + 3 i \sqrt{3}$ $-8+3isqrt3$

$(2 + \sqrt{- 3}) (- 1 + \sqrt{- 12}) \Rightarrow$ $(2 + sqrt(-3))(-1+sqrt(-12))=>$ use: $i = \sqrt{- 1} \Rightarrow$ $i= sqrt(-1) =>$

where i by definition is the imaginary part of a complex number:

$= (2 + i \sqrt{3}) (- 1 + i \sqrt{12}) \Rightarrow$ $= (2 + isqrt3)(-1 + isqrt12)=>$ simplify $\sqrt{12}$ $sqrt12$ :

$= (2 + i \sqrt{3}) (- 1 + 2 i \sqrt{3}) \Rightarrow$ $= (2 + isqrt3)(-1 + 2isqrt3)=>$ expand:

$- 2 + 4 i \sqrt{3} - i \sqrt{3} + 2 i^{2} {\sqrt{3}}^{2} \Rightarrow$ $-2 + 4isqrt3 -isqrt3+2i^2sqrt3^2=>$ simplify,note: $i^{2} = - 1$ $i^2 = -1$ :

$- 2 + 3 i \sqrt{s} 3 - 6 \Rightarrow$ $-2 + 3isqrts3-6=>$ simplify:

$- 8 + 3 i \sqrt{3}$ $-8+3isqrt3$