Question

Divide and express the result in standard form. 8/7-i

Answer 1

$i=\sqrt{-1}\to i^2=-1\ (i-the\ imaginary\ unit)\\----------------------\\\\\frac{8}{7-i}\\\\use\ (a-b)(a+b)=a^2-b^2\\\\\frac{8}{7-i}\cdot\frac{7+i}{7+i}=\frac{56+8i}{7^2-i^2}=\frac{56+8i}{49-(-1)}=\frac{56+8i}{49+1}=\frac{56+8i}{50}=\frac{56}{50}+\frac{8}{50}i\\\\=\boxed{\frac{28}{25}+\frac{4}{25}i}$

Answer 2

Assuming the problem is 8/(7-i) you would multiply the fraction by (7+i)/(7+i)
This would then simplify to 8(7+i)/50 which can be simplified down to 4(7+i)/25