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

1 Answer
Dec 6, 2015

Answer:

#-3/17+13/17i#

Explanation:

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.