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square roots of -100

Guest Feb 21, 2017

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 #2
avatar+18777 
+20

square roots of -100

 

\(\begin{array}{|rcll|} \hline && \sqrt{-100} \\ &=& \sqrt{ 100\cdot (-1)} \\ &=& 10 \cdot \sqrt{ -1 } \\ &=& 10 \cdot \sqrt{ -1 } \quad & | \quad \sqrt{z} = \sqrt{-1+0\cdot i} = \sqrt{-1} = \pm i \\ &=&10 \cdot (\pm i) \\ &=&\pm i\cdot 10 \\ \hline \end{array} \)

 

laugh

heureka  Feb 21, 2017
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 #1
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it will be +10i or -10i

it is impossible to have a real number as a square root of a negative number

Guest Feb 21, 2017
 #2
avatar+18777 
+20
Best Answer

square roots of -100

 

\(\begin{array}{|rcll|} \hline && \sqrt{-100} \\ &=& \sqrt{ 100\cdot (-1)} \\ &=& 10 \cdot \sqrt{ -1 } \\ &=& 10 \cdot \sqrt{ -1 } \quad & | \quad \sqrt{z} = \sqrt{-1+0\cdot i} = \sqrt{-1} = \pm i \\ &=&10 \cdot (\pm i) \\ &=&\pm i\cdot 10 \\ \hline \end{array} \)

 

laugh

heureka  Feb 21, 2017

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