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Simplify: (1+i)/(2-i)?
everytime i do it i get (1/5) + (2/5)i but when i search the problem the only answer showing up is (1/5) + (3/5)i
Im pretty sure its one of those 2 choices i have written
4 Answers
- Anonymous9 years agoFavorite Answer
(1+i) / (2-i)
= (1+i) (2+i) / (2-i) (2+i)
= (2 + 2i + i -1) / 4 + 1
= (1 + 3i) / 5.
It's (1/5) + (3/5)i.
- RogueLv 79 years ago
(1+i)/(2-i)
Multiply the fraction by 1 using the root pair of the denominator in this case (2 + i )/(2 + i)
=> (1+i)/(2-i) * (2+i)(2+i)
use normal foil rules remembering +i * +i = -1 and -i * + i = +1
=> (2 + i+ 2i -1)/(4 +2i - 2i +1)
=> (1 + 3i)/5
=> 1/5 + (3/5)i
