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20 votes
20 votes
Uh help please dont know whats wrong step by step will help a lot

Uh help please dont know whats wrong step by step will help a lot-example-1
User KENdi
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1 Answer

18 votes
18 votes

let's keep in mind that i² = -1, and let's use the conjugate of the denominator.


\cfrac{2+5i}{3-2i}\cdot \cfrac{3+2i}{3+2i}\implies \cfrac{(2+5i)(3+2i)}{\underset{\textit{difference of squares}}{(3-2i)(3+2i)}}\implies \cfrac{6+4i+15i+10i^2}{(3)^2~~ - ~~(2i)^2} \\\\\\ \cfrac{6+19i+10(\stackrel{i^2}{-1})}{9~~ - ~~(2^2 i^2)}\implies \cfrac{6+19i-10}{9~~ - ~~4(\underset{i^2}{-1})}\implies \cfrac{-4+19i}{9+4}\implies -\cfrac{4}{13}+\cfrac{19i}{13}

User Tim Yao
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