Ejercicio 254 – Solucionario Baldor

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DESCARGA

CAPITULO XXXII

CANTIDADES IMAGINARIAS

Ejercicio 254

Simplificar

$\begin{matrix} \sqrt{- 4} + \sqrt{- 16} & = \sqrt{(- 1) (2^{2})} + \sqrt{(- 1) (4^{2})} \\ = 2 \sqrt{- 1} + 4 \sqrt{- 1} \\ = 2 i + 4 i \\ = 6 i \end{matrix}$
$\begin{matrix} \sqrt{- 25} + \sqrt{- 81} - \sqrt{- 49} & = \sqrt{(- 1) (5^{2})} + \sqrt{(- 1) (9^{2})} - \sqrt{(- 1) (7^{2})} \\ = 5 \sqrt{- 1} + 9 \sqrt{- 1} - 7 \sqrt{- 1} \\ = 5 i + 9 i - 7 i \\ = 7 i \end{matrix}$
$\begin{matrix} 2 \sqrt{- 9} + 3 \sqrt{- 100} & = 2 \sqrt{(- 1) (3^{2})} + 3 \sqrt{(- 1) (1 0^{2})} \\ = 2.3 \sqrt{- 1} + 3.10 \sqrt{- 1} \\ = 6 i + 30 i \\ = 36 i \end{matrix}$
$\begin{matrix} 3 \sqrt{- 64} - 5 \sqrt{- 49} + 3 \sqrt{- 121} & = 3 \sqrt{(- 1) (8^{2})} - 5 \sqrt{(- 1) (7^{2})} + 3 \sqrt{(- 1) {(11)}^{2}} \\ = 3.8 \sqrt{- 1} - 5.7 \sqrt{- 1} + 3.11 \sqrt{- 1} \\ = 24 i - 35 i + 33 i \\ = 22 i \end{matrix}$
$\begin{matrix} 2 \sqrt{- a^{2}} + \sqrt{- a^{4}} + \sqrt{- a^{6}} & = 2 \sqrt{(- 1) (a^{2})} + \sqrt{(- 1) (a^{4})} + \sqrt{(- 1) (a^{6})} \\ = 2 a \sqrt{- 1} + a^{2} \sqrt{- 1} + a^{3} \sqrt{- 1} \\ = 2 a i + a^{2} i + a^{3} i \\ = i (2 a + a^{2} + a^{3}) \end{matrix}$
$\begin{matrix} \sqrt{- 18} + \sqrt{- 8} + 2 \sqrt{- 50} & = \sqrt{(- 1) (2) (3^{2})} + \sqrt{(- 1) (2) (2^{2})} + 2 \sqrt{(- 1) (2) (5^{2})} \\ = 3 \sqrt{- 1} \sqrt{2} + 2 \sqrt{- 1} \sqrt{2} + 2.5 \sqrt{- 1} \sqrt{2} \\ = 3 \sqrt{2} i + 2 \sqrt{2} i + 10 \sqrt{2} i \\ = 15 \sqrt{2} i \end{matrix}$
$\begin{matrix} 3 \sqrt{- 20} - 2 \sqrt{- 45} + 3 \sqrt{- 125} & = 3 \sqrt{(- 1) (5) (2^{2})} - 2 \sqrt{(- 1) (5) (3^{2})} + 3 \sqrt{(- 1) (5) (5^{2})} \\ = 3.2 \sqrt{5} \sqrt{- 1} - 2.3 \sqrt{5} \sqrt{- 1} + 3.5 \sqrt{5} \sqrt{- 1} \\ = 6 \sqrt{5} i - 6 \sqrt{5} i + 15 \sqrt{5} i \\ = 15 \sqrt{5} i \end{matrix}$
$\begin{matrix} \sqrt{- a^{4}} + 4 \sqrt{- 9 a^{4}} - 3 \sqrt{- 4 a^{4}} & = \sqrt{(- 1) (a^{4})} + 4 \sqrt{(- 1) (3^{2}) (a^{4})} - 3 \sqrt{(- 1) (2^{2}) (a^{4})} \\ = a^{2} \sqrt{- 1} + 4.3 a^{2} \sqrt{- 1} - 3.2 a^{2} \sqrt{- 1} \\ = a^{2} i + 12 a^{2} i - 6 a^{2} i \\ = 7 a^{2} i \end{matrix}$