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

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Answer 1 · 2015-10-24T20:31:21

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

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

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

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