Question

Divide the complex number: 7i/8+i
(i= imaginary #)
Show work?

Answer 1

Multiply top and bottom by the conjugate: \(\frac{7i}{8+i}\times\frac{8-i}{8-i}=\frac{56i+7}{65}=7+\frac{56}{65}i\).

Answer 2

Thanks ^_^

Answer 3

You're welcome! :)

Answer 4

\[\Large \frac{7i}{8+i}\]



\[\Large \frac{(7i)(8-i)}{(8+i)(8-i)}\]



\[\Large \frac{(7i)(8-i)}{(8+i)(8-i)}\]



\[\Large \frac{(7i)(8)+(7i)(-i)}{(8+i)(8-i)}\]



\[\Large \frac{(7i)(8)+(7i)(-i)}{(8)(8)+(8)(-i)+(i)(8)+(i)(-i)}\]



\[\Large \frac{56i-7i^2}{64-8i+8i-i^2}\]



\[\Large \frac{56i-7i^2}{64-8i+8i-(-1)}\]



\[\Large \frac{56i-7i^2}{64-8i+8i+1}\]



\[\Large \frac{7+56i}{65}\]



\[\Large \frac{7}{65}+\frac{56}{65}i\]



\[\Large So\frac{7i}{8+i}=\frac{7}{65}+\frac{56}{65}i\]

Answer 5

Oh sorry I made a typo in the last step. Nice work and Latex Jim!!