Question 133075
{{{((1+i)/i) - ((3)/(4-i))}}}


On the common denominator, you missed it by THAT much...


{{{i(4-i)=4i-(i^2)=4i-(-1)=4i+1=1+4i}}}, so:


{{{(((1+i)(4-i))/(1+4i)) - ((3i)/(1+4i))=((4+3i+1)-3i)/(1+4i)=5/(1+4i)}}}


Now you need the conjugate of the denominator in order to rationalize the denominator:


{{{(5/(1+4i))((1-4i)/(1-4i))=(5-20i)/(1+16)=(5+20i)/17}}}


For your other problem, I think you mean:


{{{sqrt(-15)sqrt(-15)}}}, which is {{{(i*sqrt(15))(i*sqrt(15))=i^2*15=-15}}}