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Simplify $\displaystyle\frac{1-i}{2+3i}$, where $i=\sqrt{-1}$ is the imaginary unit.

 Jan 15, 2018
 #1
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\(\frac{1-i}{2+3i}\)     Multiply  top/bottom by   2 - 3i

 

[ 1  - i  ] [ 2 - 3i ]  /  [ ( 2 + 3i) ( 2 - 3i)  ]  

 

[ 2 - 2i - 3i + 3i^2  ] /  [ 4  - 9i^2 ]

 

[ 2  -  3  - 2i -  3i  ]  / [  4 + 9 ]

 

[ -1  - 5i  ] / [ 13 ] 

 

 

cool cool cool

 Jan 15, 2018

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