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

1 Answer
mason m
Dec 6, 2015

-3/17+13/17i−317+1317i

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)3+i1−4i=3+i1−4i(1+4i1+4i)=3+12i+i+4i21+4i−4i−16i2=1+13i+4i21−16i2

Recall that i=sqrt(-1)i=√−1, so i^2=-1i2=−1.

=(1+13i+4(-1))/(1-16(-1))=(1-4+13i)/(1+16)=(-3+13i)/17=-3/17+13/17i=1+13i+4(−1)1−16(−1)=1−4+13i1+16=−3+13i17=−317+1317i

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

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