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Compute (1 + i)/(2 - i)(3 + i).

 Aug 21, 2024
 #1
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We start off with the expression \((1+i) \over ( 2-i) (3+i) \)

 

Now, let's expand and simplify the bottom, we get \((1+i) \over ( 7 -i) \)

 

Now let's start the rationalization process. Multiply the top and bottom by the conjugate of the denominator, and we get

\(\frac{(1+i)}{ (7-i)} \cdot \frac{(7+i)}{(7+i)} \\ =\frac{6 +8i}{50}\)

 

Dividing top and bottom by 2 and canceling out the 2, we get

\(\frac{1}{25}( 3 + 4i) \) which is our final answer. 

 

Thanks! :)

 Aug 21, 2024
edited by NotThatSmart  Aug 21, 2024

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