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What does #(2i)/(4-5i)# equal?

1 Answer

Oct 24, 2015

#(2i)/(4-5i) = -10/41+8/41 i#

Explanation:

Multiply numerator and denominator by the conjugate #(4+5i)# of the denominator and simplify...

#(2i)/(4-5i) = (2i(4+5i))/((4-5i)(4+5i)) = (-10+8i)/(4^2+5^2) = (-10+8i)/(16+25) = (-10+8i)/41 = -10/41+8/41 i#

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