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Simplify (1 - i)/(2 + 3i - 4 + 5i), where i^2 = -1.

 Jul 27, 2022
 #1
avatar+2270 
+1

Combine like terms: \({1 - i \over 8i -2}\)

 

Multiply by \({8i + 2 \over 8i + 2}\)\({(1 -i)(8i + 2) \over {(8i - 2)(8i + 2)}}\)

 

Expand: \({-8i^2 + 6i + 2 \over 64i^2 - 4}\)

 

Substitute \(i^2 = -1\)\({8 + 6i + 2 \over -64 - 4}\)

 

Combine like terms: \({10 + 6i \over -68}\)

 

Simplify: \(\color{brown}\boxed{- 5 - 3i \over 34}\)

 Jul 27, 2022
 #2
avatar+45 
+1

BuilderBoi, your answer is correct, however I'm pretty sure to express that answer as a complex number you would write it as 

\(\frac{-5}{34}-\frac{3}{34}i\)

 Jul 28, 2022

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