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Simplify (1 - i)/(1 + i), where i^2 = -1.

 Dec 5, 2019
 #1
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+1

Simplify by multiplying first bracket with the other bracket

(1-i)*(1-i) FOIL 

1-i-i+i^2

1-2i+i^2

you said i^2=-1 

subsituite 

1-2i+(-1)

Combine like terms 

-2i+0 = -2i 

 Dec 5, 2019
 #2
avatar+23905 
+2

Simplify \(\dfrac{1 - i}{1 + i}\), where \(i^2 = -1\).

 

\(\begin{array}{|rcll|} \hline && \mathbf{ \dfrac{1 - i}{1 + i} } \\\\ &=& \left(\dfrac{1 - i}{1 + i} \right)\times \left(\dfrac{1 - i}{1 - i}\right) \\\\ &=& \dfrac{(1 - i)^2}{(1 + i)(1-i)} \\\\ &=& \dfrac{1^2-2i+i^2}{1^2-i^2} \quad & | \quad i^2 = -1 \\\\ &=& \dfrac{1^2-2i-1}{1^2+1} \\\\ &=& \dfrac{ -2i }{2} \\\\ &=& \mathbf{-i} \\ \hline \end{array}\)

 

laugh

 Dec 5, 2019

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