How do you divide #(8i)/(-1+3i)#?

1 Answer
Jul 26, 2016

Answer:

I found: #2.4-0.8i#

Explanation:

To perform this division between complex numbers we need first to transform the denominator into a Real number; to do that we can multiply and divide by the complex conjugate of the denominator:
#(8i)/(-1+3i)*color(red)((-1-3i)/(-1-3i))=((8i)(-1-3i))/((-1+3i)(-1-3i))=#
#=(-8i+24)/(1+9)=#
remembering that #i^2=-1#
Now we can perform the division having in the denominator a simple real number:
#=(24-8i)/10=24/10-8/10i=2.4-0.8i#