Question

How do you simplify `(5 + 8i) /( 6- i)`?

Answer 1

`22/37+53/37i`

Explanation:

Multiply the conjugate.

`(5+8i)/(6-i)xx(6+i)/(6+i)=(30+5i+48i+8i^2)/(36+6i-6i-i^2)=(30+53i+8i^2)/(36-i^2)`

Remember that because `i=sqrt1,i^2=-1`.

`(30+53i+8(-1))/(36-(-1))=(30-8+53i)/(36+1)=(22+53i)/37=22/37+53/37i`

Note that I've written the answer in the complex form `a+bi`.