How do you divide $(2-4i)/(4-3i)$ ?

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Answer 1 · 2016-01-27T02:11:26

$4/5 -2/5 i$

Remember: $i^2 = -1$

Given $(2-4i)/(4-3i)$

We can simplify this expression by multiply by the conjugate of the denominator

$((2-4i)/(4-3i))color(red)(( (4+3i)/(4+3i))$

Expand the expression, then combine like terms,

$(8+6i -16i -12i^2) /(16-12i +12i -9i^2)$

$= (8 -16i -12(-1))/(16-9(-1))$

$= (20 -10i)/(25)$

$= (20)/25 -(10)/25 i$

$=4/5 -2/5 i$

How do you divide (2-4i)/(4-3i)(2-4i)/(4-3i)?