divide (3+2i)/(-4+5i). express answer in standard form

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25-08-2016
Mathematics

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divide (3+2i)/(-4+5i). express answer in standard form

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dalendrk dalendrk · Answer 1 · 2016-08-27T18:35:53-04:00

dalendrk dalendrk

27-08-2016

\(\dfrac{3+2i}{-4+5i}=\dfrac{(3+2i)(-4-5i)}{(-4+5i)(-4-5i)}=\dfrac{-12-15i-8i-10i^2}{(-4)^2-(5i)^2}\\\\=\dfrac{-12-23i+10}{16+25}=\dfrac{-2-23i}{41}=-\dfrac{2}{41}-\dfrac{23}{41}i\)

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