How do you divide $3+i div 1-4i$ ?

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Answer 1 · 2015-12-06T04:37:31

$-3/17+13/17i$

Multiply by the complex conjugate.

$(3+i)/(1-4i)=(3+i)/(1-4i)((1+4i)/(1+4i))=(3+12i+i+4i^2)/(1+4i-4i-16i^2)=(1+13i+4i^2)/(1-16i^2)$

Recall that $i=sqrt(-1)$ , so $i^2=-1$ .

$=(1+13i+4(-1))/(1-16(-1))=(1-4+13i)/(1+16)=(-3+13i)/17=-3/17+13/17i$

Notice how the answer is written in the $a+bi$ form of a complex number.

How do you divide 3+i div 1-4i3+i div 1-4i?