# math

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Simplify: (1+i)/(2-i)

A)(1/3)+(2/3i)
B)(1/5)+(2/5i)
C)(1/3)+(i)
D)(1/5)+(3/5i)
I have no clue please explain

• math -

similar to "rationalizing the denominator"

Multiply top and bottom by 2+i and remember that i^2 = -1
(1+i)/(2-i) x (2+i)/(2+i)
= (2+i+2i+i^2)/(4-i^2)
= (2+3i-1)/(4-(-1))
= (1+3i)/5

• math -

btw, the choice that fits my answer would be D, they simply split it into 2 parts.
I don't know why they would do that

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